THE  FUNDAMENTAL  PRINCIPLES 
OF  CHEMISTRY 


THE    FUNDAMENTAL    PRINCIPLES 

OF 

•CHEMISTRY' 


AN  INTRODUCTION  TO  ALL   TEXT-BOOKS 
OF  CHEMISTRY 


BY 


WILHELM    OSTWALD 
u 


AUTHORIZED  TRANSLATION  BY 

HARRY   W.    MORSE 


LONGMANS,   GREEN,  AND    CO. 

91  AND  93  FIFTH  AVENUE,  NEW   YORK 

LONDON,  BOMBAY,   AND  CALCUTTA 

1909 


COPYRIGHT,  1909,  BY 
LONGMANS,  GREEN,  &  Co. 


All  rights  reserved 


THE    UNIVERSITY    PRESS,  CAMBRIDGE,  U.S.A. 


PREFACE 

Two  tasks  are  set  for  the  workers  in  any  science.  One  of  these 
is  to  enrich  the  chosen  field  by  the  discovery  of  new  facts  and  the 
statement  of  new  experiences.  The  other  task  is  no  less  important, 
but  its  value  is  perhaps  not  so  evident  at  first  glance.  It  is  to  ar- 
range the  facts  already  known  in  the  best  order  and  to  bring  out 
the  relations  between  them  as  clearly  as  possible.  Whenever 
progress  in  the  first  of  these  tasks  has  been  rapid  the  second  be- 
comes the  more  necessary,  for  it  offers  the  only  possible  way  of 
attaining  mastery  over  the  manifold  separate  experiences  and  of 
bringing  the  science  as  a  whole  into  a  convenient  and  serviceable 
form. 

The  extraordinary  development  of  the  experimental  side  of  the 
science  of  Chemistry  has  in  some  measure  thrust  into  the  back- 
ground the  work  which  has  been  done  on  the  methodical  side. 
This  work  has  not  been  wholly  lost,  but  an  examination  of  the 
various  theories  which  have  been  advanced  in  the  past  few  dec- 
ades, especially  in  the  field  of  organic  chemistry,  indicates  that 
most  of  them  were  born  of  the  necessity  of  a  day  and  that  they 
were  ephemeral  in  their  influence.  A  desire  for  generalization  is 
an  important  and  justified  one,  and  the  only  reason  for  the  un- 
satisfactory outcome  of  all  these  theories  is  to  be  sought,  in  my 
opinion,  in  a  fundamental  error.  Hypothetical  assumptions  were 
used  in  their  development.  Hypotheses  were  set  up  in  each  case 
with  special  reference  to  the  phenomenon  to  be  explained,  and  I 
believe  that  the  right  way  has  been  obscured  in  many  instances. 

Indication  of  the  right  way  is  given  by  the  experience  of  other 
sciences  which  are  older  and  simpler  than  Chemistry  and  which 
have  therefore  already  attained  the  necessary  ripeness.  Mathe- 


1  Q  J.9.9.9 


vi  PREFACE 

matics,  Geometry,  and  Mechanics  began  an  examination  of  their 
fundamental  principles  years  ago,  and  a  firm  foundation  has  now 
been  set  up  for  each  of  these  sciences.  The  present  time  is  de- 
cidedly philosophical  in  its  trend,  and  in  the  past  few  years  this 
task  has  been  taken  up  with  renewed  vigour.  The  results  of  this 
labour  form  a  valuable  and  fruitful  portion  of  modern  scientific 
knowledge.  The  end  sought  is  the  discovery  of  final  truths  and 
the  relations  between  them,  and  these,  when  found,  give  safe  foun- 
dation for  further  investigation.  This  does  not  mean  the  setting  up 
of  analogies  and  hypotheses,  but  the  careful  analysis  of  concepts 
and  indication  of  the  general  facts  of  experience  from  which  they 
are  derived. 

In  Chemistry  research  of  this  kind  has  been  undertaken  only 
casually  and  over  small  portions  of  the  field.  Franz  Wald  is  one 
of  the  independents  who  has  been  working  along  this  line  for  many 
years.  General  appreciation  of  the  fundamental  character  of  such 
investigation  extends  very  slowly  indeed.  Three  years  ago,  on  the 
occasion  of  the  Faraday  lecture,  I  made  an  attempt  to  arouse  the 
interest  of  chemists  in  these  matters,  but  the  result  was  not  very 
encouraging.  But  few  expressions  of  opinion  were  offered  on  this 
occasion,  and  these  were  largely  contradictory  in  nature.  It  was 
quite  evident  that  the  question  at  issue  was  not  clearly  understood, 
and  the  entire  matter  was  strange,  even  to  chemists  of  note.  But 
I  know  from  personal  experience  that  patient  and  continued  labour 
can  accomplish  wonders  even  when  the  case  seems  hopeless.  One 
must  wait  for  the  right  time,  and  I  am  convinced  that  the  time  for 
this  matter  has  arrived. 

The  present  book  has  for  its  object  the  presentation  of  the 
actual'  fundamental  principles  of  the  science  of  Chemistry,  their 
meaning  and  connection,  as  free  as  possible  from  irrelevant  addi- 
tions. It  represents  in  a  sense  the  carrying  out  of  a  thought  ex- 
pressed in  the  preface  to  my  "  Grundlinien  der  Anorganischen 
Chemie."  It  was  there  suggested  that  it  was  possible  to  work 
out  a  chemistry  in  the  form  of  a  rational  scientific  system,  with- 


PREFACE  vii 

out  bringing  in  the  properties  of  individual  substances.  In  order 
to  accomplish  this,  many  exceedingly  elementary  things  must  be 
restated  with  special  reference  to  the  connection  between  them^ 
and  it  was  also  necessary  to  bring  out  many  new  connections  in 
regions  hitherto  untouched.  The  difficulties  which  arise  during 
such  a  first  attempt  became  very  clear  to  me  as  the  work  progressed, 
and  I  recognise  them  fully.  They  may  serve  as  my  excuse  for 
the  many  irregularities  in  presentation  which  will  be  found  in  the 
book.  There  was  no  doubt  in  my  mind  that  the  work  must  be 
done  sooner  or  later,  and  this  is  my  justification  for  undertaking 
it  and  carrying  it  out  to  the  best  of  my  ability. 

The  pedagogic  importance  of  the  matter  is  of  the  same  order 
as  its  scientific  importance.  Questions  concerning  fundamental 
principles  meet  the  teacher  at  every  step,  and  the  mental  char- 
acter of  the  developing  chemist  is  frequently  determined  by  the 
way  in  which  they  are  answered. 

This  will  explain  my  choice  of  a  sub-title.  I  do  not  mean  that 
the  beginner  should  absorb  the  entire  contents  of  this  book  before 
he  learns  about  oxygen  and  chlorine  as  chemical  individuals.  I 
am  quite  of  the  opinion  that  a  close  personal  acquaintance  with 
a  considerable  number  of  important  and  characteristic  substances 
is  and  always  must  be  the  fundament  of  all  instruction  in  Chem- 
istry. But  when  this  acquaintanceship  has  once  been  obtained 
it  can  be  nothing  but  an  advantage  to  the  student  to  point  out  to 
him  the  great  connections  by  which  these  separate  facts  are  bound 
together  into  a  unit;  they  may  then  be  shown  free  from  all  that 
is  individual  and  accidental,  united  into  a  great,  simple  whole. 

The  book  should  be  a  guide  to  the  teacher.  It  may  serve  to 
show  him  how  such  generalizations  are  to  be  handled  and  how 
they  can  be  woven  into  his  daily  instruction  in  elementary  chem- 
istry. Generalizations  are  the  fundamental  base  of  the  chemical 
symphony;  and  the  various  separate  parts  may  be  varied  accord- 
ing to  need  or  desire.  To  make  use  of  another  simile,  —  Generali- 
zations are  the  bony  skeleton  of  the  chemical  body,  and  the  teacher 


viii  PREFACE 

must  always  let  the  bones  appear  through  the  individual  chemical 
facts  if  he  wishes  to  make  of  his  teaching  a  true  work  of  art. 

In  two  other  books  ("  Grundlinien  der  Anorganischen  Chemie" 
and  "  Schule  der  Chemie  ")  I  have  endeavoured  to  show  practical 
solutions  of  this  problem.  I  have  often  said  that  there  may  be 
any  number  of  equally  good  solutions  for  it,  and  I  hope  that  the 
present  volume  may  serve  as  proof  of  this.  May  these  "  Funda- 
mental Principles  "  be  of  aid  to  each  teacher  in  finding  his  own 
personal  solution. 

W.  OSTWALD. 
GROSS-BOTHEN,  September,  1907. 


CONTENTS 


PAGES 

PREFACE   .  v-viii 


CHAPTER  I 

BODIES,   SUBSTANCES,   AND   PROPERTIES 

1.  Bodies.  2.  Laws  of  nature.  3.  Arbitrary  properties  and  specific 
properties.  4.  Substances  and  mixtures.  5.  Chemical  processes. 
6.  Energy.  7.  Mechanical  properties.  Volume.  8.  Volume.  9.  Weight. 
10.  The  conservation  of  weight.  11.  Mass.  12.  Density  and  specific 
volume.  13.  Volume  energy  and  pressure.  14.  Quantities  and  intensi- 
ties. 15.  Heat  and  temperature.  16.  Compressibility.  17.  Expansi- 
bility   1-25 


CHAPTER  II 

THE   THREE   STATES 

18.  The  three  states.  19.  Solid  bodies.  Crystals.  20.  Elasticity  and 
energy  of  shape.  21.  Surface  energy.  22.  Change  of  volume  in  solids. 
23.  Expansion  of  crystals.  24.  Liquids.  25.  Surface  energy.  26.  Vis- 
cosity. 27.  Volume.  28.  Water  an  exception.  29.  Measurement  of 
density.  30.  Liquid  crystals.  31.  Gases.  32.  Boyle's  Law.  33.  The 
Law  of  Gay-Lussac.  34.  Absolute  temperature  and  the  absolute  zero. 
35.  The  gas  law 26-46 


CHAPTER  III 

MIXTURES,   SOLUTIONS,   AND   PURE   SUBSTANCES 

36.  States.  37.  Mixtures.  38.  Methods  of  Separation.  39.  Properties 
of  mixtures.  40.  Liquid  solutions.  41.  Solutions  other  than  liquid 
ones.  42.  Mixtures  of  liquids  with  solids.  43.  Liquid  mixtures. 

44.  Mixtures  of  gases.     45.  Foams 47-59 

ix 


x  CONTENTS 

CHAPTER  IV 

CHANGE   OF   STATE   AND    EQUILIBRIUM 

(a)   The  Equilibrium  Liquid-Gas  PAOEa 

46.  Equations  of  condition.  47.  The  liquefaction  of  gases.  48.  Pure 
substances  and  solutions.  49.  Reversibility.  50.  Equilibrium.  51.  Sat- 
uration. 52.  The  influence  of  pressure.  53.  The  vapour  pressure 
of  water.  54.  Diagram.  55.  Change  of  volume  during  evaporation. 
56.  Heat  of  vaporization.  57.  The  measurement  of  quantity  of  heat. 
58.  Entropy.  59.  The  critical  point.  60.  Phases.  61.  Degrees  of 
freedom.  62.  Sublimation.  63.  Suspended  transformation  .  .  .  60-80 

(b)   The  Equilibrium  Solid-LiquM 

64.  Melting  and  solidification.  65.  The  effect  of  pressure.  66.  Supercool- 
ing. 67.  The  law  of  the  displacement  of  equilibrium  ~ 80-84 

(c)  Equilibrium  between  the  three  States 

68.  The  triple  point.  69.  The  equilibrium  law.  70.  The  vapour  pressure 
curve  at  the  triple  point 85-89 

(d)   The  Equilibrium  Solid-Solid 

71.  Allotropism.  72.  The  influence  of  pressure.  73.  The  phenomena  of 
suspended  transformation.  74.  The  step  by  step  law.  75.  The  vapour 
pressure  of  allotropic  forms  89-95 


CHAPTER  V 

SOLUTIONS 

76.  General  considerations.  77.  Kinds  of  solutions.  78.  Solutions  of 
gases.  79.  Diffusion.  80.  The  applicability  of  the  gas  laws.  81.  Partial 
pressure.  82.  The  gas  constant  as  applied  to  solutions.  83.  Other 
properties  of  gas  solutions.  84.  Separation  of  a  gas  solution  into  its 
constituents.  85.  Semi-permeable  diaphragms.  86.  Separation  step 
by  step.  87.  Analogy  with  change  of  state.  88.  Pure  substances. 
89.  Solutions  of  liquids  in  gases.  90.  Saturation.  91.  The  influence 
of  pressure.  92.  The  effect  of  temperature.  93.  The  phase  rule. 
94.  Components.  95.  Composition.  96.  Liquid  solutions.  97.  Solutions 
of  gases  in  liquids.  98.  The  law  of  absorption.  99.  Solutions  of  liquids 
in  liquids.  100.  Unlimited  solubility.  101.  Maxima  and  minima. 
102.  Limited  solubility.  103.  The  effect  of  temperature  and  pressure. 


CONTENTS  xi 

PAGES 

104.  The  critical  point  for  solutions.  105.  The  separation  of  liquid 
solutions  into  their  components.  106.  The  vapour  of  solutions. 
107.  Distillation.  108.  Fractional  distillation.  109.  Singular  points. 
110.  Singular  solutions.  111.  Gaseous  solutions  produced  from  liquid 
substances.  112.  The  vapour  of  partially  miscible  liquids.  113.  Pos- 
sible cases.  114.  The  double  line.  115.  Equilibrium  with  solid  sub- 
stances. 116.  The  effect  of  pressure  and  temperature.  117.  Liquid 
solutions  of  solid  substances.  118.  The  eutectic  point.  119.  Connec- 
tion with  the  ordinary  solubility  curve.  120.  Solubility  at  the  melting 
point.  121.  The  solubility  of  allotropic  forms.  122.  Solutions  of  higher 
order.  123.  The  general  properties  of  singular  points 96-165 


CHAPTER  VI 

ELEMENTS   AND   COMPOUNDS 

124.  Hylotropy.  125.  Chemical  processes  in  the  narrower  sense.  126.  Ele- 
ments. 127.  The  reversibility  of  chemical  processes.  128.  The  con- 
servation of  the  elements.  129.  Synthetic  processes.  130.  The  law 
of  continuity.  131.  Graphic  representation.  132.  Solutions  made  up 
of  phases  in  the  same  state.  133.  Two  solids.  134.  Solutions  of  dis- 
similar states.  135.  One  gas  and  one  liquid.  136.  The  temperature 
axis.  137.  Boiling  point  curves.  138.  Two  liquid  phases.  139.  One 
gas  phase  and  two  liquid  phases.  140.  The  melting  point  curve. 
141.  The  sublimation  curve.  142.  More  complicated  cases.  143.  The 
appearance  of  chemical  compounds.  144.  Summary.  145.  The  effect 
of  temperature.  146.  More  general  conditions.  147.  Two  gases. 
148.  Energy  content.  149.  The  law  of  constant  proportions.  150.  Two 
liquids.  151.  Two  solids.  152.  Analytical  methods.  153.  Gases. 
154.  Liquids.  155.  Triple  systems.  156.  Individual  cases.  157.  The 
evolution  of  a  gas.  158.  Liquid  separation.  159.  Solid  separation. 
160.  The  solution  remains  homogeneous 166-246 


CHAPTER  VII 

THE    LAW   OF    COMBINING   WEIGHTS 

M 

161.  The  law  of  constant  proportions.  162.  Combining  weights.  163.  Ter- 
nary compounds  and  those  of  higher  order.  164.  The  combining 
weights  of  compound  substances.  165.  The  law  of  rational  multi- 
ples. 166.  Chemical  formulae.  167.  Chemical  equations.  168.  Methods 
of  determining  combining  weights.  169.  The  indefiniteness  of  the 
combining  weights.  170.  The  general  relations  of  the  combining 
weights 247-264 


xii  CONTENTS 

CHAPTER  VIII 

COLLIGATIVE   PROPERTIES 

PAGES 

171.  The  law  of  gas  volumes.  172.  The  relation  to  the  combining  weights. 
173.  Combining  weight  and  molar  weight.  174.  Numerical  values. 
175.  The  properties  of  dilute  solutions.  176.  Molar  lowering  of  the 
vapour  pressure.  177.  Osmotic  pressure.  178.  Numerical  relations. 
179.  Interpretation.  180.  The  effect  on  freezing  point.  181.  The 
importance  of  the  .solution  laws.  182.  Colligative  properties  .  265-289 

CHAPTER  IX 

REACTION   VELOCITY   AND   EQUILIBRIUM 

183.  Reaction  velocity.  184.  Variable  velocity.  185.  The  law  of  re- 
action velocity.  186.  Catalysers.  187.  Ideal  catalysers.  188.  Chemi- 
cal equilibria.  189.  More  than  one  phase.  190.  The  law  of  mass  action. 
191.  Explanation  of  anomalous  cases.  192.  The  quantitative  investi- 
gation of  equilibria.  193.  Is  equilibrium  affected  by  a  catalyser? 
194.  Induction  and  deduction 290-314 

CHAPTER  X 

ISOMERISM 

195.  The  relation  between  composition  and  properties.  196.  Poly- 
morphism. 197.  The  determination  of  the  stability  of  polymorphic 
forms.  198.  Isomerism.  199.  Metamerism  and  polymerism.  200.  Con- 
stitution. 201.  Valence 315-330 

CHAPTER  XI 

THE   IONS 

202.  Salt  solutions  and  ions.  203.  Faraday's  law.  204.  The  concept  of 
ions  considered  chemically.  205.  Univalent  and  polyvalent  ions. 
206.  The  molar  weight  of  salts.  207.  The  application  of  the  phase 
law.  208.  Electrolytic  dissociation  331-341 


INDEX    .  343-349 


THE 

OF  CHEMISTRY 

CHAPTER  I 
BODIES,  SUBSTANCES,  AND  PROPERTIES 

1.  BODIES.  —  Chemistry  is  a  part  of  inorganic  natural  science. 
It  has  to  do  with  those  objects  in  the  universe  which  are  without 
life,  —  with  non-living  bodies. 

Those  parts  or  divisions  of  space  which  are  evidently  different 
from  their  surroundings  are  called  bodies.  They  exhibit  these 
differences  to  us  primarily  through  the  impressions  which  our 
organs  of  sense  receive  from  them.  Beside  this  immediate  im- 
pression through  our  senses  we  make  use  also  of  indirect  expe- 
rience by  observing  the  mutual  action  of  various  bodies  on  each 
other,  but  all  our  impressions  depend  finally  on  direct  sense  im- 
pressions received  from  the  bodies  involved. 

The  concept  of  a  body  has  arisen  because  certain  properties 
are  found  to  be  common  to  the  same  portion  of  space,  and  because 
these  properties  persist  in  spite  of  spatial  changes  in  the  system. 
I  recognise  the  body  which  I  call  a  flask,  primarily  by  the  way  in 
which  light  reaches  my  eyes  from  a  certain  spot.  I  can  then 
satisfy  myself  that  my  sense  of  touch  receives  a  definite  impres- 
sion at  the  same  spot,  and  that  the  impression  so  received  is  in 
accord  with  the  visual  one.  I  find  further  that  I  must  do  a  certain 
amount  of  work  in  order  to  bring  about  a  change  in  the  position 
of  this  portion  of  space  (characterized  by  these -proper ties)  with 
respect  to  its  surroundings.  The  flask  is  said  to  be  heavy.  If  I 
perform  this  necessary  amount  of  work,  all  the  properties  men- 

1 


2  FUNDAMENTAL  PRINCIPLES  OF  CHEMISTRY 

tioned,  and  many  others  beside,  move  together  into  a  new  position 
and  may  be  four\d  there  unchanged  in  their  relations  to  one  an- 
other. Daily  experience  lias  taught  me  that  certain  properties  are 
connected  and  appear  together,  and  the  sum  of  all  such  experience 
is  contained  in  the  concept  body.  Experiences  of  this  kind,  which 
are  frequently  and  regularly  repeated,  are  called  laws  of  nature. 
It  is  a  law  of  nature  that  certain  properties  are  so  connected  that 
they  cannot  be  transported  independently  from  one  place  to  an- 
other. They  always  move  together.  Another  expression  for  such 
repeated  experiences  is  concept.  A  concept  is  a  law  of  nature 
expressed  in  an  abbreviated  form.  It  is  usually  expressed  in  a 
word  or  a  name,  but  in  science  there  are  many  other  ways  of  in- 
dicating concepts.  Chemical  formulae  are  not  words,  but  we  shall 
use  them  later  as  a  means  of  representing  very  definite  concepts. 

The  word  "  body  "  is  used  to  designate  the  following  concept : 
Certain  definite  properties  (especially  colour,  lustre,  shape,  and 
weight)  are  connected  as  a  matter  of  experience. 

2.  LAWS  OF  NATURE.  —  The  name  natural  law  is  not  a  very 
fortunate  one,  for  it  suggests  an  analogy  with  human  laws  which 
may  lead  to  wholly  false  impressions.  By  a  law  of  nature  we 
mean  that  as  a  matter  of  experience  there  is  a  relation  between 
certain  phenomena,  such  that  they  occur  either  together  or  in 
regular  sequence  in  time.  That  law  of  nature  which  says  that 
bodies  exist  expresses  the  experience  that  we  always  find  the  prop- 
erty of  weight  at  the  same  place  in  space  where  we  find  lustre, 
hardness,  a  definite  shape,  etc.,  and  that  all  of  these  properties 
can  only  be  moved  from  place  to  place  together. 

It  is  of  course  quite  impossible  for  us  to  examine  all  the  cases 
where  such  a  relation  exists,  and  we  can  therefore  never  state  with 
absolute  certainty  that  such  a  connection  has  always  existed  in 
the  past  and  always  will  persist  in  the  future.  But  we  have  found 
such  a  condition  in  all  the  cases  which  we  have  had  time  to  ex- 
amine, and  we  therefore  assume  that  we  shall  find  it  true  in  the 
future.  The  conclusion  about  bodies  and  their  properties  has 


BODIES,  SUBSTANCES,   AND   PROPERTIES  3 

been  under  examination  for  a  long  time  by  a  very  great  number 
of  observers,  and  it  has  always  been  confirmed.  There  is  there- 
fore a  very  high  degree  of  probability  that  it  will  always  be  con- 
firmed in  the  future. 

A  law  of  nature  is  therefore  to  be  considered  as  the  expectation 
of  a  connection  between  possible  experiences.  This  expectation 
is  founded  on  the  fact  that  in  every  case  which  has  been  observed 
up  to  the  present  time  the  same  connection  has  appeared.  And 
the  oftener  the  expectation  is  tested  with  confirmatory  result  the 
greater  is  the  probability  of  its  future  fulfilment. 

It  is  evident  that  the  concept  of  a  natural  law  contains  nothing 
of  unconditionality  nor  of  necessity.  Observation  of  various  ex- 
periences, related  in  time  and  space,  is  the  foundation  of  such  a 
law,  and  the  prediction  of  similar  future  relations,  founded  on  such 
observations,  gives  the  law  its  chief  importance.  Natural  laws  are 
therefore  much  like  guide-posts,  which  tell  us  what  to  expect  as 
a  result  of  certain  experiences,  or  what  conditions  must  be  ful- 
filled in  order  that  certain  things  may  happen. 

The  last  relation  explains  the  extraordinary  importance  of  these 
natural  laws;  for,  with  a  knowledge  of  these  laws  as  a  basis,  we 
can  not  only  predict  future  events  to  a  certain  extent,  we  can  also 
cause  them  arbitrarily  to  occur. 

For  example,  if  the  room  is  cold,  we  put  coal  into  the  furnace. 
This  does  not  of  itself  make  the  room  any  warmer,  but  if  we  kindle 
the  coal  and  let  it  burn,  the  room  becomes  more  comfortable.  On 
the  basis  of  our  knowledge  of  the  natural  law  that  coal  can  be 
kindled  and  gives  out  heat  when  it  burns,  we  know  in  advance 
that  we  can  warm  the  room  by  putting  coal  into  the  furnace  and 
setting  it  afire.  Every  time  we  apply  this  law,  and  in  so  doing 
test  its  truth,  we  find  it  confirmed,  and  we  are  so  convinced  of  its 
reliability  that  we  have  no  hesitation  in  spending  the  money  neces- 
sary to  provide  a  supply  of  coal  for  winter. 

3.   ARBITRARY    PROPERTIES    AND    SPECIFIC    PROPERTIES.  - 
Not  all  the  properties  which  we  find  in  a  given  body  have  this 


4  FUNDAMENTAL  PRINCIPLES  OF  CHEMISTRY 

peculiarity  of  remaining  together.  There  is  no  way  by  which  we 
can  change  the  weight  of  a  body,  unless  we  take  away  a  part  of  it 
or  add  a  piece  to  it,  but  we  can  change  its  temperature,  its  electrical 
condition,  its  motion,  etc.  We  can  therefore  distinguish  between 
two  classes  of  properties:  those  which  persist  with  the  body  and 
whose  sum  makes  up  the  concept  of  the  body,  and  those  which 
can  be  arbitrarily  attached  to  or  taken  away  from  it.  The  first  are 
called  specific  properties,  the  others  accidental  or  arbitrary  prop- 
erties. The  distinction  is  so  important  that  it  is  the  basis  for  the 
separation  of  two  of  the  sciences :  Chemistry  has  to  do  with  specific 
properties,  while  the  arbitrary  properties  are  the  province  of 
Physics. 

We  can,  for  example,  make  any  body  hot  or  cold,  we  can  elec- 
trify it,  we  can  illuminate  it  with  red  or  blue  light,  we  can  magne- 
tize it,  etc.  In  all  of  these  cases  we  are  dealing  with  arbitrary 
properties,  and  their  study  belongs  to  Physics,  and  not  directly  to 
Chemistry.  But  the  metallic  nature  of  silver,  its  good  conductivity 
for  heat  and  electricity,  its  stability  in  air  and  at  high  tempera- 
tures, its  solubility  in  nitric  acid,  —  these  we  cannot  take  away 
singly  or  change  one  at  a  time.  The  study  of  such  properties  be- 
longs to  Chemistry. 

The  amount  of  a  body  and  its  external  shape  are  arbitrary 
properties,  for  they  can  be  changed  at  will.  In  Chemistry  we 
therefore  study  bodies  without  paying  any  attention  to  amount 
and  shape.  Bodies  which  are  considered  only  in  connection  with 
their  specific  .properties  are  called  substances,  and  they  form  the 
materials  for  the  study  of  Chemistry.  Substances  are  said  to  be 
alike  chemically  when  they  have  similar  specific  properties. 

4.  SUBSTANCES  AND  MIXTURES.  —  If  our  description  of  the 
specific  properties  of  a  body  is  to  be  definite,  it  is  evident  that 
these  properties  must  be  the  same  in  all  parts  of  the  body  under 
consideration ;  otherwise  there  would  be  no  way  of  deciding  which 
of  the  properties,  appertaining  to  different  parts  of  the  body, 
should  be  chosen  as  defining  the  body. 


BODIES,  SUBSTANCES,  AND  PROPERTIES  5 

By  no  means  all  of  the  bodies  which  exist  or  which  we  make 
have  properties  which  are  the  same  in  all  of  their  parts.  If  we  ex- 
amine the  various  pebbles  which  form  the  bed  of  a  brook  we  shall 
find  among  them  some  which  are  the  same  in  every  part,  so  that 
any  piece  chipped  off  has  the  same  colour,  hardness,  density,  etc., 
as  the  whole  pebble  or  any  other  piece  of  it.  But  we  shall  also  find 
other  pebbles  which  show  immediately  by  their  variegated  colours 
that  they  consist  of  several  materials,  and  a  closer  investigation 
will  show  that,  in  general,  the  parts  which  differ  in  colour  differ 
also  in  their  other  properties.  Bodies  of  the  first  sort  are  called 
homogeneous  bodies ;  those  belonging  to  the  second  class  are  called 
mixtures. 

In  what  follows  we  shall  confine  ourselves  expressly  to  the  homo- 
geneous bodies,  since  they  are  the  only  ones  with  definite  specific 
properties.  Substances  are  always  homogeneous  bodies.  We 
say,  for  instance,  that  knife-blades,  files,  hatchets,  scissors,  and 
similar  instruments  all  consist  of  the  same  substance,  —  steel ; 
because  the  specific  properties  of  all  these  bodies,  such  as  hardness, 
lustre,  density,  rusting  in  moist  air,  etc.,  are  the  same.  To  the 
chemist  a  broken  knife  is  no  different  from  a  perfect  one,  and  a 
dull  one  is  just  like  a  sharp  one,  for  they  are  all  steel;  but  to  a 
mechanic  there  is  an  important  difference.  The  same  object  is 
often  of  interest  to  several  sciences,  but  each  one  has  a  separate 
set  of  interests  in  the  body  and  examines  a  different  set  of  rela- 
tions. When  a  knife  is  magnetic  it  interests  a  physicist;  as  a  his- 
torical object  it  may  appeal  to  an  archaeologist  or  an  antiquarian; 
as  an  implement  it  would  be  an  object  of  study  for  an  ethnologist, 
etc.  Each  of  these  scientists  will  examine  the  same  object  from  a 
different  point  of  view. 

5.  CHEMICAL  PROCESSES.  —  It  is  quite  possible  to  change  the 
specific  properties  of  a  substance,  but  all  its  properties  change  at 
the  same  time.  We  say  in  this  case  that  one  substance  disappears, 
and  that  another,  having  new  properties,  appears.  If  we  pour 
nitric  acid  over  silver,  brown  fumes  of  unpleasant  odour  are  formed 


6  FUNDAMENTAL   PRINCIPLES   OF   CHEMISTRY 

which  were  not  present  before,  while  the  silver  disappears  after 
a  short  time,  leaving  a  colourless  liquid  behind.  This  liquid  is 
different  from  the  nitric  acid  which  was  used,  for  nitric  acid  re- 
mains clear  when  a  solution  of  common  salt  is  added  to  it,  while 
the  same  salt  solution  produces  a  precipitate  in  the  liquid  which 
contains  the  silver.  This  precipitate  is  white  at  first,  arid  changes 
to  gray  in  the  light. 

Processes  like  this  are  known  in  great  number.  The  combus- 
tion of  coal,  the  rusting  of  iron,  changes  in  animal  and  vegetable 
substances  exposed  to  the  air, — these  are  examples  of  such  changes. 
All  of  these  phenomena  have  in  common  the  fact  that  certain  sub- 
stances disappear  and  others  with  other  properties  are  formed,  and 
changes  of  this  sort  are  called  chemical  reactions.  In  order  to  de- 
cide whether  a  chemical  process  has  taken  place  or  not,  we  must 
know  the  properties  of  the  substances  with  which  we  started,  and 
compare  them  with  the  properties  of  the  substances  which  appear 
later.  If  they  are  different,  a  chemical  reaction  has  taken  place. 
The  change  in  properties  is  not  always  so  striking  as  in  the  cases 
cited.  It  is  often  necessary  to  measure  the  properties  of  the  sub- 
stances involved  before  and  after  the  experiment  in  order  to 
discover  differences  and  render  judgment  on  them. 

6.  ENERGY.  —  The  properties  of  various  bodies  were  charac- 
terized as  the  relation  which  these  bodies  bear,  directly  or  in- 
directly, to  our  organs  of  sense.  Now  our  sense  organs  are  affected 
by  only  a  single  general  condition,  which  is  that  a  transfer  of 
energy  takes  place  between  them  and  the  outside  world.  All  the 
properties  of  bodies  are  therefore  definable  in  terms  of  energy. 

We  mean  by  energy  everything  which  can  be  produced  from 
work  or  which  can  be  transformed  into  work.  We  have  had  for 
a  long  time  a  law  of  conservation  for  mechanical  work,  which 
states  that  it  is  impossible  to  increase  the  amount  of  work  in  a 
closed  system  by  any  sort  of  mechanical  contrivance.  And  when 
we  learned  to  transform  work  into  heat,  electricity,  light,  etc.,  we 
found  that  the  same  law  is  applicable  to  all  of  these.  From  a  given 


BODIES,   SUBSTANCES,   AND   PROPERTIES  7 

amount  of  mechanical  work  it  is  possible  to  obtain  only  certain 
definite  amounts  of  electrical  work,  light,  etc.,  and  when  these  are 
changed  back  into  mechanical  work,  exactly  equivalent  amounts 
of  the  latter  are  obtained.  Energy  may  therefore  be  considered 
as  a  substance,  in  the  sense  that  it  is  under  all  circumstances  con- 
served and  persistent.  This  substance  can  be  transformed  into 
the  most  varied  forms,  but  its  amount  is  neither  increased  nor 
diminished  by  any  number  of  transformations. 

Certain  forms  of  energy  are  permanently  bound  to  bodies  and 
condition  their  weight,  mass,  and  volume.  These  things  are  not 
energy  themselves,  but  they  are  properties  or  factors  of  correspond- 
ing forms  of  energy,  which  are  called  gravitational  energy,  energy  of 
motion,  and  volume  energy.  Other  forms  of  energy  can  be  added 
to  a  given  body  and  taken  away  from  it  again,  and  electrical  energy, 
light,  and  heat  are  of  this  kind.  It  will  be  seen  from  this  that  the 
difference  in  the  processes  which  have  been  classified  as  physical 
and  chemical  depends  primarily  on  the  nature  of  the  energy-forms 
which  take  part  in  the  process.  We  shall  find  later,  from  a  study 
of  chemical  phenomena,  that  there  is  a  special  chemical  energy, 
which  is  connected  with  the  mass,  weight,  and  volume  of  bodies. 
It  is,  in  fact,  because  of  the  inseparable  union  of  the  elements 
which  make  up  the  concept  body  that  chemical  phenomena  appear 
only  in  bodies,  that  is,  in  systems  possessed  of  weight,  mass,  and 
volume. 

The  inorganic  natural  sciences  can  be  most  completely  and 
easily  classified  by  reference  to  the  various  forms  of  energy.  First 
of  all,  there  are  just  as  many  special  branches  of  science  as  there 
are  forms  of  energy.  We  distinguish  mechanics,  heat,  electricity, 
magnetism,  optics  (which  seems  of  late  to  be  developing  into  a 
branch  of  electricity),  and  chemistry.  There  are,  furthermore, 
other  sciences  which  depend  on  the  mutual  relation  between 
several  forms  of  energy.  Fifteen  pairs  can  be  made  from  the  six 
branches  named,  and  five  of  them  include  chemistry.  We  there- 
fore have  mechano-chemistry,  thermo-chemistry,  electro-chemistry, 


8  FUNDAMENTAL   PRINCIPLES   OF  CHEMISTRY 

magneto-chemistry,  and  photo-chemistry,  beside  pure  chemistry. 
We  shall  study  especially  mechanical  energy  and  heat,  and  their 
influence  on  chemical  reactions  through  pressure  and  tempera- 
ture. Only  mechano-chemistry  and  thermo-chemistry  are  of 
especial  importance  in  this  relation,  but  we  shall  have  occasion 
to  take  into  account  the  most  important  phenomena  of  electro- 
and  photo-chemistry  also.  It  can  hardly  be  said  that  there  is  a 
magneto-chemical  branch  of  science,  and  magnetic  energy  has  in 
general  only  slight  relation  to  any  form  of  energy  except  electrical 
energy. 

If  we  were  constructing  a  system,  we  should  next  consider  those 
sciences  in  which  three  or  more  different  forms  of  energy  are  of 
importance,  the  forms  being  connected  by  a  mutual  series  of  trans- 
formations. So  far  no  one  has  developed  such  a  system,  and  it  has 
been  found  sufficient  to  classify  cases  belonging  here  under  one 
of  the  pair-groups  mentioned  above.  We  shall  find  ourselves  con- 
tinually dealing  with  simultaneous  effects  of  chemical,  mechanical, 
and  thermal  energy. 

7.  MECHANICAL  PROPERTIES.  VOLUME.  —  In  accordance  with 
the  above  classification  we  have  first  of  all  to  take  up  the  mechanical 
properties  of  substances.  Some  of  these  properties  are  common 
to  all  substances,  others  appear  only  in  individual  cases.  The 
general  properties  are  volume,  weight,  and  mass. 

These  properties  are  in  one  sense  arbitrary,  inasmuch  as  all 
bodies  are  divisible  at  will.  But  when  a  body  is  divided,  the  value 
of  each  of  these  three  properties  is  divided  in  the  same  proportion. 
For  when  we  divide  a  body  in  such  a  way  that  the  new  piece  has 
half  the  volume  of  the  original  one,  we  find  that  its  weight  and  its 
mass  have  also  half  of  their  original  values.  The  absolute  values 
of  volume,  weight,  and  mass  are  therefore  arbitrary,  but  when  one 
of  the  three  is  varied  the  others  vary  in  the  same  proportion.  Any 
relation  between  these  three  values  is  therefore  not  an  arbitrary 
one  but  a  constant  for  any  particular  substance,  and  this  relation 
is  a  specific  property. 


BODIES,   SUBSTANCES,   AND   PROPERTIES  9 

The  result  thus  stated  is  an  expression  of  another  very  im- 
portant law  of  nature,  that  is  to  say,  it  is  an  oft-repeated  and 
invariably  confirmed  experience.  It  has  been  expressed  in  the 
concept  matter,  and  weight,  mass,  and  volume  have  accordingly 
been  called  the  fundamental  properties  of  matter.  Such  a  mode 
of  designation  has  no  disadvantages  as  long  as  the  experiential 
origin  of  the  concept  is  kept  clearly  in  mind.  But  the  idea  that 
there  is  something  more  in  the  concept  of  matter  than  the  expres- 
sion of  a  set  of  experiences  and  their  reduction  to  a  law  of  nature 
has  persisted  from  earlier  times.  Matter  is  looked  upon  as  some- 
thing originally  existing,  which  is  at  the  bottom  of  all  phenomena 
and  in  a  sense  independent  of  them  all.  The  concept  of  matter 
can  be  shown,  however,  to  be  made  up  of  the  simpler  concepts 
weight,  mass,  and  volume,  and  it  is  certainly  less  fundamental  than 
these.  The  law  of  the  invariable  connection  of  these  properties 
has  already  been  expressed  in  the  concepts  body  and  substance,  so 
there  is  no  necessity  for  the  formation  of  a  new  concept  to  express 
the  same  thing.  The  word  "  matter  "  is  so  closely  connected  with 
the  ideas  mentioned  above  that  it  is  not  advisable  to  retain  it ;  we 
shall  therefore  not  make  any  use  of  it  whatever. 

A  practical  knowledge  of  our  law  must  next  be  obtained  by  find- 
ing how  weight,  mass,  and  volume  are  determined  and  measured. 

8.  VOLUME.  —  In  general  we  measure  a  quantity  by  comparing 
it  with  a  definite  unchangeable  quantity  of  the  same  kind,  thus 
finding  the  relation  of  the  quantity  to  be  measured  to  the  constant 
"  unit."  We  must  therefore  first  of  all  set  up  the  units  of  volume, 
weight,  and  mass. 

The  cubic  centimetre  (ccm.  or  cm.3)  is  the  unit  of  volume  for  all 
scientific  purposes.  It  was  originally  defined  by  reference  to  the 
length  of  a  bar  such  that  10,000,000  of  these  lengths  would  reach 
from  one  of  the  poles  of  the  earth  to  the  equator.  This  length  is 
called  a  metre  (m.).  The  hundredth  part  of  the  metre  is  called  a 
centimetre  (cm.),  and  a  cube  measuring  one  centimetre  on  each  edge 
is  the  unit  of  volume  given  above. 


10  FUNDAMENTAL   PRINCIPLES  OF  CHEMISTRY 

In  order  to  insure  the  greatest  possible  constancy  to  the  unit 
bar,  it  is  made  of  platinum-iridium,  the  most  stable  metal  known, 
and  it  is  preserved  at  Paris  with  especial  care.  Similar  metre  rods 
are  preserved  in  the  capitals  of  most  of  the  countries  of  the  world, 
and  the  length  of  each  of  these  copies  has  been  very  carefully  com- 
pared with  that  of  the  original  metre  at  Paris.  If  the  Paris  standard 
rod  should  be  destroyed  in  any  way,  the  unit  metre  would  not  be 
lost,  since  the  length  of  many  other  rods  is  accurately  known  i.i 
terms  of  the  original  standard. 

Each  body  has  a  definite  volume,  measured  and  expressed  i:i 
cubic  centimetres,  and  represented  by  a  number.  If  the  body  has 
a  definite  geometric  form,  its  volume  can  be  found  by  measuring, 
for  example,  its  edges  in  centimetres  and  calculating  its  volume 
from  these  measurements  with  the  aid  of  a  geometric  formula.  In 
the  majority  of  cases  bodies  have  irregular  shapes;  we  shall  see 
later  how  their  volumes  can  be  determined  under  these  conditions. 
The  volume  of  a  body  is  often  defined  as  the  space  which  it 
occupies. 

9.  WEIGHT.  —  By  the  weight  of  a  body  we  understand  pri- 
marily the  force  with  which  it  tends  to  fall.  This  force  differs 
slightly  at  different  points  on  the  earth,  becoming  smaller  as  the 
equator  is  approached  and  with  elevation  above  the  earth's  sur- 
face. But  observation  has  given  us  the  general  natural  law  that 
such  differences  affect  all  bodies  in  the  same  proportion.  So  when 
two  bodies  have  the  same  weight  at  any  point  on  the  earth  they 
are  also  alike  in  this  property  at  any  other  point.  It  is  necessary 
to  distinguish  between  absolute  weight  and  relative  weight.  The 
former  is  measured  by  the  force  exerted  by  a  body  on  its  support, 
or  by  the  force  with  which  it  tends  to  fall,  and  this  is  variable  from 
place  to  place.  The  relative  weight  expresses  how  many  times  the 
absolute  weight  of  the  body  is  larger  or  smaller  than  the  absolute 
weight  of  a  body  chosen  arbitrarily  once  for  all,  —  the  unit  of  weight. 
Such  a  unit  of  weight  changes  in  absolute  value  from  place  to 
place,  but  changes,  according  to  the  above  law,  in  the  same  pro- 


BODIES,   SUBSTANCES,   AND   PROPERTIES  11 

portion  as  every  other  body.  The  relative  weight  is  therefore  in- 
dependent of  position,  and  is  a  definite  number  for  any  given  body. 

The  standard  for  the  determination  of  relative  weights  is  a 
piece  of  platinum-iridium,  preserved,  like  the  standard  metre, 
near  Paris,  and  protected  from  destruction  by  many  copies,  which 
have  been  scattered  over  the  world  after  careful  comparison  with 
the  original.  It  is  called  the  kilogramme  (kgm.).  The  thousandth 
part  of  this  weight  is  used  as  the  scientific  standard,  and  it  is  called 
a  gramme  (gm.). 

The  original  intention  was  to  make  the  kilogramme  such  that 
a  cube  of  water  at  its  maximum  density  (+  4°  C.)  with  an  edge 
of  one  metre  should  weigh  exactly  a  thousand  kilogrammes.  A 
cube  of  water  a  centimetre  on  the  edge  would  then  weigh  a 
gramme.  Although  the  determination  of  this  relation  between 
units  was  certainly  not  made  as  exactly  at  the  time  of  its  meas- 
urement as  it  can  be  at  the  present  time,  the  desired  relation 
turns  out  to  have  been  accidentally  very  nearly  fulfilled.  We  shall 
therefore  take  the  relative  weight  of  a  cubic  centimetre  of  water 
at  +  4°  C.  as  being  one  gramme. 

In  what  follows  we  shall  have  to  deal  almost  exclusively  with 
relative  weights;  we  shall  therefore  for  brevity  make  use  of  the 
word  "  weight  "  in  the  sense  of  relative  weight,  and  in  the  few 
cases  where  absolute  weight  is  involved  we  shall  designate  the  latter 
by  its  full  name. 

The  weight  of  any  body  is  determined  with  the  aid  of  the  equal- 
arm  balance,  by  placing  the  body  to  be  weighed  in  one  pan  and 
adding  known  weights  to  the  other  until  equilibrium  is  reached. 
The  sum  of  the  known  weights  is  then  equal  to  the  weight  of  the 
body. 

For  water  the  unit  volume  and  the  unit  weight  are  the  same, 
that  is,  both  units  refer  to  the  same  body  of  water.  The  num- 
ber which  indicates  the  weight  in  grammes  of  any  amount  of 
water  indicates  at  the  same  time  its  volume  in  cubic  centi- 
metres. This  statement  is  exactly  true  only  at  a  temperature 


12  FUNDAMENTAL   PRINCIPLES   OF  CHEMISTRY 

of  +  4°  C. ;  later  we  shall  take  up  variations  corresponding  to 
other  temperatures. 

10.  THE  CONSERVATION  OF  WEIGHT.  —  We  have  a  remarkable 
and  very  general  natural  law  about  weight :  no  matter  what  processes 
are  carried  out  on  a  given  body,  its  weight  is  never  changed.  A  body 
retains  its  weight  whether  it  is  warm  or  cold,  positively  or  nega- 
tively electrified,  etc. ;  and  even  chemical  reactions  have  no  effect 
on  weight,  provided  no  substances  having  weight  are  added  or 
taken  away.  If  all  chance  of  loss  or  gain  by  this  means  is  ex- 
cluded by  shutting  up  the  substances  in  question  in  proper  vessels, 
a  careful  determination  of  the  weight  shows  that  no  change  takes 
place  even  with  deep-seated  changes  in  the  chemical  nature  of  the 
inclosed  substances.  This  is  called  the  law  of  the  conservation  of 
weight. 

This  law  is  sometimes  called  the  law  of  the  conservation  of 
matter,  but  this  is  an  unscientific  expression,  since  the  concept  of 
matter  is  not  defined  with  sufficient  exactness  to  warrant  its  use 
(see  Sec.  7). 

The  law  of  the  conservation  of  weight  has  lately  been  subjected 
to  a  thorough  investigation.  Various  substances  which  could 
react  chemically  with  one  another  were  sealed  up  in  glass  vessels, 
and  the  total  weight  of  the  apparatus  was  determined  before  and 
after  chemical  reaction  between  the  substances.  A  general  con- 
firmation of  the  law  was  the  result,  in  the  sense  that  the  probable 
changes  were  smaller  than  the  hundred  thousandth  part  of  the 
total  weight  involved.  Very  small  changes  were,  however,  noticed 
which  seem  larger  than  the  probable  error  of  observation.  These 
changes  were  all  in  the  direction  of  a  decrease  in  weight,  so  that 
the  total  weight  was  smaller  after  the  reaction  than  before.  In 
case  this  result  is  confirmed,  it  must  be  concluded  that  the  law  of 
the  conservation  of  weight  is  not  absolutely  exact,  and  deviations 
from  it  in  the  sense  of  a  decrease  in  weight  as  a  consequence  of 
chemical  action  must  be  admitted. 

Although  this  question  has  only  lately  been  scientifically  ex- 


BODIES,   SUBSTANCES,   AND   PROPERTIES  13 

amined,  and  while  it  is  by  no  means  decided,  these  experiments 
have  been  mentioned  because  they  show  that  the  law  of  the  con- 
servation of  weight  has  nothing  "  fundamental  "  or  necessary 
about  it.  Such  a  necessity  has  often  been  asserted  on  false  theo- 
retical grounds,  but  as  a  matter  of  fact  this  law  has  the  same  char- 
acter as  all  other  natural  laws.  It  is  only  a  summary  of  certain 
experiences,  and  its  accuracy  is  therefore  limited  by  the  range 
and  accuracy  of  these  experiences.  Constant  improvement  in  the 
methods  of  observation  which  are  used  in  scientific  work  is  con- 
tinually widening  the  range  of  experience  and  its  exactness  as  well, 
and  it  happens  very  often  that  laws  which  seemed  perfectly  exact 
at  an  earlier  time,  when  methods  of  measurement  were  less  perfect 
than  they  now  are,  show  exceptions  on  more  careful  observation. 
A  new  problem  then  arises:  the  deviations  and  exceptions  must 
be  measured  and  compared,  and  the  new  relations  thus  found 
must  be  expressed  in  a  new  law,  if  possible. 

11.  MASS.  —  The  mass  of  a  body  is  determined  by  its  behaviour 
with  respect  to  causes  of  motion.  Two  masses  are  said  to  be  equal 
when  each  is  given  the  same  velocity  by  the  expenditure  of  the 
same  amount  of  work,  and  the  masses  of  two  bodies  which  are  not 
equal  are  measured  by  the  amounts  of  work  which  are  necessary 
to  give  them  the  same  velocity.  Mass  and  work  are  proportional 
in  this  sense,  and  so  a  body  which  requires  ten  times  as  much  work 
to  give  it  the  same  velocity  as  that  of  another  body  has  ten  times 
its  mass.  As  a  matter  of  experience  we  always  find  the  same  re- 
lation between  two  masses,  no  matter  what  velocity  they  have.  It 
is  therefore  a  natural  law  that  mass  is  independent  of  the  velocity.* 

The  unit  of  mass  is  primarily  the  mass  of  a  gramme  of  platinum- 
iridium.  Experience  has  shown  a  natural  law  to  hold  here:  the 
mass  of  any  body  always  has  a  constant  relation  to  its  weight,  wholly 

*  Only  lately  the  law  that  mass  is  independent  of  velocity  has  become 
doubtful  for  velocities  nearly  equal  to  the  velocity  of  light.  Bodies  in  the 
ordinary  sense  of  the  word  do  not  have  velocities  of  this  order  of  magnitude, 
and  we  can  therefore  apply  this  law  in  the  study  of  chemistry  without  danger 
of  any  measurable  error. 


14  FUNDAMENTAL   PRINCIPLES   OF  CHEMISTRY 

independent  of  all  the  other  properties  of  the  body.  It  is  con- 
sequently unnecessary  to  state  the  material  from  w^iich  the  unit 
of  mass  is  made,  and  the  unit  of  mass  is  therefore  the  mass  of  a 
gramme. 

The  fact  just  mentioned,  that  mass  and  weight  always  have  the 
same  relation  in  any  body,  permits  us  to  deduce  the  law  of  the  con- 
servation of  mass  from  that  of  the  conservation  of  weight.  For  if 
weight  is  unchanged,  for  example,  by  chemical  reaction,  then 
mass  is  also  unchanged,  since  it  can  be  calculated  from  weight  by 
multiplication  by  a  constant  factor,  which  does  not  change  under 
any  known  conditions.  As  a  matter  of  fact  the  law  of  the  conserva- 
tion of  mass  can  also  be  proven  directly,  and  it  has  been  found 
of  the  same  order  of  accuracy  as  the  law  of  the  conservation  of 
weight. 

These  two  quantities,  mass  and  weight,  are,  however,  the  only 
properties  of  a  body  which  are  strictly  conservative.  All  other 
properties  can  be  varied  within  broad  or  narrow  limits.  And  this 
is  just  as  true  of  the  specific  properties  as  it  is  of  the  arbitrary 
ones.  In  the  case  of  the  latter  the  variation  can  usually  be  carried 
so  far  that  the  value  of  the  property  reaches  zero  (that  is,  the  body 
no  longer  exhibits  the  property  at  all),  while  specific  properties 
can  be  varied  only  within  definite  and  usually  rather  narrow 
limits. 

12.  DENSITY  AND  SPECIFIC  VOLUME.  —  If  we  designate  vol- 
ume by  V,  weight  by  W,  and  mass  by  M ,  we  can  have  the  six 

V    V   W  M  W          M 

relations  — ,  — ,  — ,  — ,  — ,  and  —  between  these  three  quantities. 

W  M  M   V    V          W 

All  these  relations  represent  specific  properties  of  a  substance. 
For,  inasmuch  as  the  three  properties,  volume,  weight,  and  mass 
of  any  substance,  can  only  be  changed  so  that  they  remain  pro- 
portional to  each  other,  the  relations  between  them  are  always 
independent  of  the  arbitrary  amount  and  shape  of  the  body  ex- 
amined. They  are  therefore  specific  properties  in  the  sense  of 
the  definition  given.  (Sec.  3.) 


BODIES,   SUBSTANCES,   AND   PROPERTIES  15 

We  have  iust  seen  that  —  and  —  are,  of  these  relations,  the  ones 
W        M 

which  are  the  same  for  all  bodies,  no  matter  what  their  other  prop- 
erties may  be.  The  unit  of  weight  and  the  unit  of  mass  have 
been  so  chosen  that  they  can  be  expressed  by  the  same  number, 

and  the  relation  —  (and  —  as  well)  is  therefore  always  unity.* 

Because  of  this  independence  of  all  the  other  differences  between 
bodies  this  relation  is  of  no  use  in  the  characterization  of  different 
bodies,  and  we  shall  therefore  not  have  occasion  to  refer  to  it 
again. 

Further,     -  =  —  and   —  =  — ,  because   we   have  chosen  our 
W     M  V      V 

units  so  that  W  =  M. 

Relative  weight   (W)  is  very  much  easier  to  determine  than 

V          W 

mass  (M),  and  we  therefore  in  practice  measure  —  and  — ,  even 

V       M 

when  —  or  —  is  needed  for  any  special  reason.    We  need  there- 

V          W 

fore  to  consider  only  the  relations  —  and  Jr. 

W 
The  relation  77,  that  is,  the  weight  divided  by  the  volume  or 

the  weight  of  unit  volume,  is  called  the  density  or  the  specific 
gravity. 

The  relation  — ,  the  volume  divided  by  the  weight  or  the  volume 

occupied  by  unit  weight,  is  called  specific  volume.  This  and  the 
previous  relation  —  are  reciprocal,  which  means  that  one  of  them 

is  obtained  by  dividing  unity  by  the  other.  They  therefore  ex- 
press the  same  property,  merely  being  different  in  form.  The 

*  It  must  be  remembered  that  this  equality  holds  only  when  W  is  used 
to  indicate  the  relative  weight.  Absolute  weight  varies  from  place  to  place, 
while  mass  is  invariable.  There  can  therefore  be  no  possibility  of  a  general 
equivalence  of  these  two  quantities. 


16  FUNDAMENTAL   PRINCIPLES  OF  CHEMISTRY 

density  is  the  more  commonly  used  as  the  expression  of  this  prop- 
erty, but  the  specific  volume  is  the  better  from  a  theoretical  point 
of  view.  For  while  weight  is  an  invariable  property  of  each  body, 
volume  changes  with  pressure  and  temperature.  It  is  better  to 
express  the  relation  in  such  a  way  that  the  invariable  quantity  is 

taken  as  basis.     —  is  for  this  reason  better  than  — . 

In  the  case  of  water  at  4°  C.  volume  and  weight  are  expressed 
by  the  same  number;  their  ratio  is  therefore  unity.  The  den- 
sity of  water  at  4°  is  1.00,  and  its  specific  volume  has  the  same 
value. 

The  various  substances  which  occur  in  nature,  or  can  be  made 
artificially,  show  great  variations  in  density.  Some  of  them  have 
values  as  high  as  22.5,  equivalent  to  a  specific  volume  of  0.0444. 
In  the  direction  of  small  density  there  is  no  limit  known,  for  any 
given  volume  can  be  filled  with  a  gas  as  dilute  as  we  choose.  It 
seems  probable  from  general  considerations  that  there  is  a  limit 
of  some  kind  in  this  direction,  even  though  we  have  no  means  of 
sufficient  delicacy  to  prove  it. 

13.  VOLUME  ENERGY  AND  PRESSURE.  — The  mass  of  a  body 
and  its  weight  can  be  changed  only  by  adding  to  it  or  taking  away 
from  it  amounts  of  other  bodies.  With  the  volume  it  is  different, 
for  it  can  be  changed  in  many  ways  by  uniting  certain  forms  of 
energy  with  the  body.  We  shall  have  occasion  to  examine  only 
mechanical  and  thermal  influences  in  this  connection. 

Mechanical  energy  can  appear  in  several  different  forms,  and 
we  have  here  to  deal  with  the  one  called  volume  energy.  It  takes 
part  in  the  changes  which  occur  in  the  volume  of  a  body  when 
pressure  is  applied  to  or  removed  from  the  body,  and  it  is  measured 
by  the  product  of  pressure  and  change  of  volume. 

For  instance,  work  must  be  expended  to  pump  up  a  bicycle  tire, 
and,  furthermore,  it  requires  more  and  more  work  to  send  a  pump- 
ful  of  air  into  the  tire  as  the  pressure  rises.  It  also  requires  more 
work  to  pump  up  a  large  tire  than  a  small  one,  because  the  former 


BODIES,   SUBSTANCES,  AND  PROPERTIES  17 

has  the  larger  volume.  In  order  to  calculate  the  work,  the  unit  of 
pressure  must  be  established.  The  unit  of  volume  we  have  already. 
It  is  customary  to  use  the  Atmosphere  as  the  unit  of  pressure. 
This  name  comes  from  the  use  in  previous  times  of  the  average 
pressure  exerted  by  the  air  at  the  surface  of  the  earth.  This  pres- 
sure is  measured  with  a  barometer  by  balancing  it  against  a  column 
of  mercury  of  variable  height.  A  barometer  reading  of  76  cm. 
represents  the  normal  value,  and  one  atmosphere  is  defined  as  the 
pressure  exerted  by  a  column  of  mercury  76  cm.  high. 

14.  QUANTITIES  AND  INTENSITIES.  —  Volume  and  pressure 
show  certain  characteristic  differences  in  the  way  in  which  they 
enter  calculations.  Volumes  can  be  added  indefinitely  by  simple 
physical  addition,  and  they  can  be  separated  just  as  easily.  They 
are  therefore  quantities  in  the  narrower  sense,  if  the  possibility  of 
direct  addition  and  subtraction  is  accepted  as  characteristic  of 
real  quantities.  On  the  other  hand,  pressures  cannot  be  added 
by  physical  addition,  nor  can  they  be  separated  in  the  same  way. 
If  a  mass  of  air,  for  example,  under  a  certain  pressure  is  divided 
into  two  or  more  parts  without  change  in  its  total  volume,  the 
pressure  in  each  part  is  the  same  as  that  in  the  original  mass  of 
gas.  By  bringing  together  several  bodies  under  the  same  pressure 
we  do  not  multiply  the  pressures,  but  leave  the  original  one  un- 
changed. And  when  two  different  pressures  are  combined,  the 
result  is  not  the  sum  but  a  mean  between  the  two,  which  is,  beside 
dependent  on  other  conditions. 

We  have  therefore  to  distinguish  between  quantities  which  can 
be  added,  and  values  of  another  sort,  which  are  called  intensities. 
Two  equal  quantities  give  the  double  quantity  when  they  are 
brought  together;  two  equal  intensities  result  in  an  unchanged 
intensity.  It  is,  for  example,  quite  impossible  by  any  spatial  ar- 
rangement to  give  to  the  air  which  surrounds  us,  at  a  pressure  of 
one  atmosphere,  a  larger  or  a  smaller  pressure.  Its  pressure  can 
only  be  changed  by  the  use  of  outside  energy,  as  heat,  or  some 
form  of  mechanical  energy. 
2 


18  FUNDAMENTAL   PRINCIPLES   OF  CHEMISTRY 

Important  differences  in  the  measurement  of  these  .two  values 
are  to  be  expected.  A  scale  for  the  true  quantities  is  easily  pro- 
duced by  first  making  a  number  of  equal  quantities  or  units,  and 
then  by  merely  bringing  together  two,  three,  or  more  units  finding 
the  second,  third,  etc.,  value  of  the  quantity.  A  series  of  intensi- 
ties can  evidently  not  be  made  in  this  way,  for  a  total  intensity  is 
not  changed  by  bringing  together  several  intensities  of  the  same 
value.  A  different  process  must  therefore  be  used. 

Observation  has  shown  that  intensities  are  different  when  they 
act  differently.  The  pressure  in  two  vessels  is  said  to  be  the  same 
if  they  have  no  effect  on  each  other  when  they  are  connected. 
Neighbouring  regions  of  the  atmosphere  have,  in  general,  the  same 
pressure,  and  the  air  therefore  remains  at  rest  as  long  as  this  rela- 
tion remains  unchanged. 

In  other  cases  such  regions  do  influence  each  other,  and  then 
we  say  that  the  pressures  were  different.  When  there  are  different 
pressures  at  various  points  in  the  earth's  atmosphere,  the  air  is  set 
in  motion  as  a  result  of  the  difference.  The  pressure  is  said  to  be 
higher  at  the  place  where  air  is  moving  away,  and  lower  at  points 
toward  which  the  air  is  moving. 

If  a  number  of  different  pressures  are  in  question,  each  of  them 
may  be  compared  with  all  the  others  in  the  way  just  shown.  The 
result  of  such  a  comparison  can  be  expressed  in  a  natural  law 
which  states  that  all  pressures  can  be  arranged  in  a  series  such 
that  it  begins  with  the  lowest  pressure  and  ends  with  the  highest. 
Each  pressure  between  these  falls  into  its  proper  place.  The 
special  peculiarity  of  pressure  which  appears  in  this  (and  the  same 
peculiarity  is  found  in  all  other  intensities)  can  be  expressed  in 
the  following  law:  When  one  pressure  is  higher  (or  lower)  than 
another,  and  this  other  is  higher  (or  lower)  than  a  third,  then  the 
first  pressure  is  higher  (or  lower)  than  the  third.  And  in  the 
same  way  we  can  say:  If  one  pressure  is  equal  to  another, 
and  this  other  is  equal  to  a  third,  then  the  first  pressure  is  equal 
to  the  third. 


BODIES,   SUBSTANCES,   AND   PROPERTIES  19 

These  statements  appear  self-evident.  As  a  matter  of  fact  we 
are  so  accustomed  to  use  them  that  it  is  difficult  to  believe  that 
any  other  relation  could  be  possible. 

Such  important  and  far-reaching  conclusions,  which  are  not  at 
all  self-evident,  can,  however,  be  drawn  from  these  laws,  that  it  is 
necessary  and  useful  to  state  them  carefully. 

The  numbers  form  a  similar  one-sided  series,  and  pressures  can 
therefore  be  related  to  them,  using  certain  assumptions,  and  ex- 
pressed and  measured  in  terms  of  them.  The  most  general 
arrangement  of  pressures  can  be  made  with  the  help  of  energy 
relations,  and  we  will  therefore  look  at  this  way. 

First  of  all  it  must  be  remembered  that  energy  is  a  quantity  in 
the  narrower  sense,  for  any  given  amount  of  mechanical  work 
or  heat  can  be  divided,  and  several  portions  of  the  same  kind  of 
energy  can  be  combined  into  a  single  sum. 

The  electrical  energy  which  the  subscriber  draws  from  the  wires 
is  measured  by  suitable  instruments  and  added  up,  and  every  month 
the  company's  agent  comes  around  to  read  the  meter,  and  collects 
rates  proportional  to  the  energy  used. 

Experience  has  shown  that  each  form  of  energy  can  always  be 
separated  into  two  factors,  one  of  which  has  the  properties  of  a 
quantity,  and  the  other  those  of  an  intensity.  The  first  is  called 
the  capacity  factor  or  the  quantity  factor  of  energy,  and  the  other 
is  called  the  intensity  factor.  In  order  to  set  up  a  scale  for  an  in- 
tensity factor,  what  we  do  is  to  bring  into  any  system  measured 
amounts  of  energy,  taking  care  that  the  capacity  factor  remains 
the  same.  The  intensities  resulting  from  this  method  of  procedure 
are  then  proportional  to  the  corresponding  amounts  of  energy,  and 
so  a  scale  of  intensities  is  produced. 

In  order  to  preserve  such  a  scale,  and  make  it  available  for 
future  reference,  a  special  measuring  device  is  necessary.  It  is 
customary  to  use  the  ending  "  meter  "  to  indicate  devices  for 
measuring  intensities. 

A  thermometer  is  an  instrument  for  measuring  the  intensity  of 


20  FUNDAMENTAL   PRINCIPLES  OF  CHEMISTRY 

heat,  the  temperature.  An  electrometer  is  one  for  measuring  the 
intensity  of  electrical  energy,  the  voltage.  A  manometer  is  one 
which  measures  the  intensity  of  volume  energy,  the  pressure.  All 
manometers  depend  upon  the  fact  that  a  certain  amount  of  work 
is  performed  by  the  pressure.  This  amount  depends  upon  the 
construction  of  the  instrument,  and  the  motion  so  produced  is 
made  easily  visible  by  some  special  arrangement.  The  manom- 
eter of  a  steam  engine  indicates  the  steam  pressure  in  the  boiler, 
and  it  contains  a  metal  spring  which  is  bent  by  the  pressure.  The 
spring  is  connected  to  a  pointer  by  which  the  amount  of  the  motion 
can  be  read.  The  mercury  manometer  depends  upon  the  fact  that 
a  column  of  mercury  is  supported  by  the  pressure,  the  column 
changing  its  height  until  it  is  in  equilibrium  with  the  pressure 
exerted  on  it. 

In  order  to  make  a  scale  of  intensities,  a  pressure  scale,  for 
example,  according  to  the  general  scheme  indicated  above,  a 
manometer  might  be  connected  to  a  vessel  filled  with  air.  The 
pressure  inside  and  outside  the  vessel  is  first  of  all  to  be  equalized 
by  opening  the  vessel ;  the  corresponding  reading  on  the  manom- 
eter gives  us  a  starting  point;  then  a  known  amount  of  air  is 
forced  into  the  vessel.  The  manometer  rises  and  its  position  is 
noted.  The  same  amount  of  air  is  now  added  for  the  second  time, 
and  the  new  reading  of  the  manometer  indicates  a  change  of  pres- 
sure twice  as  great  as  the  former  one.  The  next  addition  of  air 
gives  the  third  point  on  the  scale,  and  so  on.  In  the  same  way  we 
might  produce  a  pressure  scale  in  equal  steps  by  filling  the  vessel 
with  water  and  providing  it  with  a  vertical  cylindrical  tube  into 
which  equal  amounts  of  water  are  poured  one  after  the  other, 
giving  a  graded  series  of  heights  in  the  tube. 

In  all  cases  of  this  kind  equal  amounts  of  work  expended  in  the 
apparatus  are  to  be  calculated  from  the  value  of  the  intensity 
which  is  present  in  the  apparatus  at  the  time.  For  example,  the 
work  required  to  lift  the  successive  amounts  of  water  in  the  appara- 
tus just  described  will  not  be  equal  but  will  increase  as  the  height 


BODIES,   SUBSTANCES,   AND   PROPERTIES  21 

of  the  column  of  water  increases,  if  we  carry  each  amount  of  water 
from  the  lowest  level  to  the  top  of  the  column.  The  definition 
holds,  however,  if  we  consider  each  addition  of  water  to  be  car- 
ried only  from  the  level  attained  by  the  last  previous  operation. 
This  peculiarity  of  intensities  is  a  very  important  property,  which 
must  always  be  kept  carefully  in  mind. 

15.  HEAT  AND  TEMPERATURE.  —  Beside  the  mechanical  prop- 
erties of  bodies,  their  thermal  or  heat  properties  are  of  special  im- 
portance in  chemistry.  The  kind  of  energy  which  is  called  heat 
is  found  in  all  bodies,  together  with  volume,  weight,  and  mass.  We 
must  therefore  know  something  about  this  form  of  energy  in  order 
to  accurately  describe  the  properties  of  bodies.  Varying  amounts 
of  volume  energy  can  be  added  to  a  given  body  according  to  the 
pressure  exerted  on  it,  and  in  the  same  way  varying  amounts  of 
heat  can  be  added  to  a  body  according  to  the  temperature  which 
is  given  to  it.  Temperature  is  that  property  of  heat  which  indi- 
cates how  different  heats  behave  towards  one  another.  If  a  body 
loses  heat  by  contact  with  another,  we  say  that  it  had  the  higher 
temperature  and  that  the  other  had  the  lower  temperature,  and 
in  the  same  way  two  bodies  have  the  same  temperature  when 
neither  takes  away  nor  adds  heat  to  the  other.  It  will  be  seen 
that  these  are  similar  to  the  relations  found  for  pressure. 

We  recognise  by  means  of  the  thermometer  whether  or  not  a 
transfer  of  heat  takes  place.  A  thermometer  is  a  small  vessel  filled 
with  mercury  and  connected  with  a,  very  narrow  tube  in  which 
the  mercury  rises  to  a  definite  point,  which  depends  upon  expan- 
sion of  the  mercury  under  the  influence  of  a  change  of  tempera- 
ture. If  the  thermometer  is  brought  in  contact  with  a  body,  heat 
transfer  takes  place  in  general,  and  the  mercury  rises  or  sinks  as 
heat  passes  from  the  body  to  the  thermometer  or  from  the  ther- 
mometer to  the  body.  When  the  mercury  ceases  to  move,  this 
indicates  that  both  have  the  same  temperature.  Each  tempera- 
ture corresponds  to  a  definite  position  of  the  mercury.  The  tem- 
perature of  various  bodies  may  therefore  be  compared  by  means 


22  FUNDAMENTAL   PRINCIPLES   OF  CHEMISTRY 

of  a  thermometer.  In  order  to  obtain  a  common  basis  for  the  ex- 
pression of  temperature  the  following  procedure  has  been  generally 
adopted  among  scientists. 

It  has  been  shown  by  experiment  that  the  temperature  of  melting 
ice  is  always  the  same,  for  if  various  thermometers  are  placed  in 
melting  ice  and  the  mercury  heights  noted,  it  is  found  on  repeated 
experiment  that  the  mercury  in  each  thermometer  always  comes 
back  to  exactly  the  same  point. 

It  has  been  shown  in  the  same  way  that  the  temperature  of  boil- 
ing water  is  constant.* 

The  points  at  which  the  mercury  stands  in  melting  ice 
and  in  boiling  water  are  determined  for  a  given  thermometer, 
and  the  space  between  these  points  is  divided  into  100  equal 
parts.  The  ice  point  is  called  0°,  the  boiling  point  100°,  inter- 
mediate temperatures  are  correspondingly  numbered.  The  de- 
grees are  further  divided  into  tenths,  hundredths,  thousandths, 
and  so  on. 

Laws  similar  to  those  which  were  developed  in  Sec.  14  for 
pressure  will  be  found  applicable  for  temperatures  also. 

If  two  bodies  show  the  same  temperature  when  tested  with  a 
thermometer,  no  transfer  of  heat  will  take  place  between  them 
when  they  are  brought  into  direct  contact.  It  follows  from  this 
that  two  temperatures,  each  equal  to  a  third,  are  also  equal  to  each 
other.  This  principle  is  purely  one  of  experience,  and  cannot  be 
derived  from  the  general  law  that  two  quantities,  each  equal  to 
a  third,  are  also  equal  to  each  other.  Temperatures  are  not  quan- 
tities, they  are  intensities,  and  if  two  bodies  which  have  the  same 
temperature  are  brought  together  the  result  is  not  double  the 
temperature,  but  the  same.  It  must,  therefore,  be  independently 
shown  that  this  general  principle  which  is  applicable  to  'quanti- 


*  The  boiling  point  changes  with  pressure  but  always  has  the  same  value 
at  the  same  barometer  height.  Knowing  the  effect  of  a  change  in  barometric 
conditions,  we  can  take  it  into  account  and  base  our  boiling  point  on  an  ar- 
bitrarily fixed  barometric  height. 


BODIES,   SUBSTANCES,   AND   PROPERTIES  23 

ties  can  be  applied  to  temperatures  and  to  intensities  in  general. 
Experience  has  shown  the  correctness  of  such  an  application  for 
all  known  intensities. 

16.  COMPRESSIBILITY.  —  The  space  occupied  by  a  body  changes 
with  pressure  and  temperature.    It  decreases  with  increasing  pres- 
sure, and  the  proportional  amount  of  this  change  is  called  the  com- 
pressibility of  the  body.    It  is  evident  that  the  decreasing  volume 
brought  about  by  any  given  increase  of  pressure  must  be  propor- 
tional to  the  volume  occupied  by  the  body,  for  if  the  change  of 
volume  is  determined  for  the  unit  of  volume,  it  must  be  n  times  as 
great  for  n  times  unit  volume,  since  volumes  can  be  added  directly. 
For  small  changes  of  pressure  the  decrease  in  volume  is  propor- 
tional to  the  change  of  pressure ;  but  if  a  great  change  in  volume 
is  produced  by  pressure  this  proportionality  can  no  longer  be  as- 
sumed to  be  true,  for  a  body  whose  volume  has  been  made  smaller 
is  no  longer  the  same  as  the  original  body  which  occupied  a  larger 
space,  and  we  cannot  assume  that  its  properties  have  remained 
unchanged. 

Within  the  region  where  the  change  of  volume  is  proportional 
to  the  change  of  pressure  the  following  expression  for  the  com- 
pressibility holds,  p  being  the  change  of  pressure,  —  v  the  change 
of  volume,  and  V  the  original  volume:  the  coefficient  of  com- 

AJ 

pressibility  z  is  given  by  z  = — ,  that  is,  the  compressibility  is 

found  by  dividing  the  observed  change  of  volume  by  the  total  volume 
and  the  change  of  pressure.  If  V  =  1  and  p  =  1  then  z  =  —  v ; 
that  is,  the  compressibility  is  equal  to  the  change  in  volume  ex- 
perienced by  the  unit  of  volume  under  unit  pressure.  The  nu- 
merical value  of  this  property  usually  varies  greatly  with  the  nature 
of  the  body  in  question,  and  we  shall  later  consider  more  carefully 
the  principal  cases. 

17.  EXPANSIBILITY.  —  Volume  varies  with  temperature  as  well 
as  pressure,  and  here  we  can  use  an  expression  similar  to  the  one 
which  holds  for  compressibility.    The  coefficient  of  expansion  is 


24  FUNDAMENTAL  PRINCIPLES  OF  CHEMISTRY 

the  expansion  of  the  unit  of  volume  under  the  influence  of  a  change 
of  temperature  of  1  degree.  If  V  is  the  volume  and  v  the  change  of 
volume  corresponding  to  a  temperature  change  t,  the  expansibility 

i) 
a  is  expressed  by  the  formula  a  =  — . 

Here  again  the  expansion  v  is  proportional  to  the  total  volume  V, 
other  conditions  remaining  the  same.  The  same  relation,  however, 
cannot  be  premised  for  the  effect  of  temperature,  for  by  varia- 
tion in  the  temperature  a  body  acquires  different  properties,  and 
in  the  majority  of  cases  the  coefficient  of  expansion  a  has  different 
values  for  the  same  body  at  different  temperatures.  These  values 
approach  one  another  more  nearly  the  nearer  the  temperatures 
under  consideration.  They  are  said  to  be  continuous  functions 
of  the  temperature,  but  this  holds  only  when  the  body  does  not 
change  suddenly  or  discontinuously  into  another  body  under  the 
influence  of  temperature,  as  is  the  case  with  ice,  which  changes 
into  water  on  heating. 

There  are  a  few  bodies  which  decrease  their  volume  instead  of 
expanding  when  they  are  heated.  This  is,  however,  a  rare  case, 
and  the  general  rule  is  an  increase  of  volume  with  increasing 
temperature. 

If  a  body  is  inclosed  in  a  stiff  shell,  so  that  it  cannot  expand 
when  heated,  the  pressure  will  change,  and  as  a  rule  it  increases, 
since  most  bodies  increase  their  volume  on  heating.  The  same 
condition  can  evidently  be  realized  by  first  heating  the  body  at 
the  original  pressure  and  then  decreasing  its  volume  by  an  increase 
of  pressure  until  the  original  value  of  the  volume  is  reached.  Under 
these  circumstances  the  compressibility  is  a  determining  factor, 
and  therefore  only  two  of  the  three  quantities,  compressibility, 
expansibility,  and  change  of  pressure  on  heating  are  independent ; 
the  third  is  determined  by  the  two  others. 

Change  of  pressure  with  temperature  has  so  far  been  given  no 
generally  accepted  name.  Let  us  call  it  the  "  temperature  pres- 
sure," and  we  will  set  up  a  numerical  expression  for  its  value.  It 


BODIES,   SUBSTANCES,   AND   PROPERTIES  25 

is  evidently  independent  of  the  volume,  for  the  latter  is  by  definition 
to  remain  unchanged,  and  can  therefore  have  no  influence  on  the 
numerical  value  of  the  property.  We  will  find  expression  for  this 
in  our  formula.  If  a  body  has  volume  F,  its  change  of  volume  v 
with  change  of  temperature  t  is  given  by  the  equation  given  above 
as  v  =  aVt.  The  change  of  volume  with  change  of  pressure  p  is 
given  by  v  =  —  zVp,  and  by  our  definition  these  two  are  to  be 

equal,  so  aVt  =  —  zVp,  or  ~  = .     ~  is  our  temperature  pressure; 

t          z      t 

it  is  the  change  of  pressure  at  constant  volume  for  unit  change  of 
temperature,  and  its  value  is  the  relation  of  compressibility  to 
expansibility.  It  is  evident  then  that  any  one  of  these  three  quan- 
tities can  be  calculated  when  the  two  others  are  known. 

All  three  are  dependent  on  temperature  and  pressure,  as  has 
been  shown.  They  are,  beside,  specific  properties  of  substances, 
that  is,  they  are  equal  for  the  same  substances.  It  would  be  better 
to  say  that  those  substances  are  said  to  be  the  same  in  which  these 
properties  have  equal  values. 


CHAPTER  II 
THE  THREE   STATES 

18.  THE   THREE    STATES.  —  Beside  the  properties  which  be- 
long equally  to  all  bodies,  there  are  others  which  are  evident  in  very 
different  degrees  in  different  bodies,  and  which  therefore  serve  to 
subdivide  bodies  into  groups  or  classes,  according  as  one  or  more 
of  these  properties  is  present  or  not.    The  totality  of  this  degree 
of  difference  is  expressed  in  the  three  states  in  which  bodies  occur. 
There  are  solid  bodies,  liquid  bodies,  and  gaseous  bodies. 

We  are  justified  in  using  the  name  "  states  "  to  indicate  these 
three  things,  because  external  peculiarities  are  of  determining  im- 
portance in  their  differentiation.  Solid  bodies  have  a  definite  shape 
of  their  own,  and  persist  in  it,  while  liquids  take  on  a  shape  which 
is  determined  by  external  causes.  Liquids  continue,  however,  un- 
changed in  volume  in  spite  of  all  changes  of  shape.  Gases  have 
neither  a  definite  shape  nor  a  definite  volume,  and  the  value  of 
these  two  properties  is  in  every  case  determined  by  the  vessel  which 
contains  them. 

Other  important  properties  are  always  connected  with  these, 
and  we  will  consider  them  somewhat  minutely. 

19.  SOLID     BODIES.      CRYSTALS.  —  Solid    bodies   are   charac- 
terized by  the  fact  that  they  have  a  definite  shape,  and  that  this 
persists  until  it  is  changed  by  work  of  some  kind.    This  shape  can 
in  some  cases  be  arbitrary  (or  accidental),  as,  for  example,  in  the 
case  of  a  glass  flask  or  a  piece  of  glass  which  is  obtained  by  break- 
ing a  vessel.    In  other  cases  regular  forms  occur,  as,  for  example, 
the  cube  and  similar  forms,  as  in  the  case  of  common  salt.    These 
peculiar  forms  are  called  crystals.  The  majority  of  solid  bodies  have 

26 


THE  THREE   STATES  27 

crystal  form,  but  often  obscured  and  made  difficult  to  recognise  by 
accidental  causes.  The  crystals  of  a  substance  may  be  either  large 
or  small  according  to  circumstances,  and  may  look  otherwise  very 
different  from  each  other ;  but  it  has  been  found  that,  in  spite  of  all 
differences  in  size  and  shape,  the  crystals  of  a  substance  always 
show  regularity.  They  consist  of  planes  which  cut  each  other  at 
the  same  angle.  For  example,  all  crystals  of  common  salt  are 
bounded  by  planes  perpendicular  to  each  other;  they  therefore 
form  cubes  and  rectangular  parallelopipedons.  If  we  imagine  the 
surfaces  which  bound  the  various  crystals  of  the  same  substance 
to  be  displaced  parallel  to  themselves  (this  will  cause  no  change  in 
the  angle  at  which  they  cut  each  other),  it  is  always  possible  to 
produce  one  definite  form.  In  the  case  of  common  salt  this  will 
be  a  cube,  and  in  all  cases  where  the  same  form  can  be  thus  pro- 
duced the  crystals  are  said  to  have  the  same  crystal  form. 

The  crystal  form  is  just  as  much  a  specific  property  of  bodies 
as  their  density  and  colour,  for  the  smallest  visible  piece  shows  the 
same  crystal  form  as  a  larger  piece  of  any  size,  provided  the  shape 
has  not  been  arbitrarily  changed. 

It  has  been  stated  (Sec.  3)  that  the  arbitrary  shape  of  a  substance 
is  not  to  be  taken  as  a  characteristic.  Here,  however,  it  is  stated 
that  the  crystal  form  is  a  specific  property  of  solid  substances. 
The  contradiction  is  only  an  apparent  one,  for  crystal  forms  are 
not  arbitrary,  but  natural.  They  result  without  human  aid  when- 
ever and  wherever  such  substances  are  produced.  Attention  has 
been  called  to  the  fact  that  the  shape  of  a  body  is  by  no  means 
completely  determined  by  its  crystalline  properties.  These  de- 
termine only  the  fact  that  it  is  bounded  by  surfaces  which  are  in- 
clined to  one  another  at  certain  angles;  the  mutual  position  of 
these  surfaces  and  the  resulting  size  and  shape  of  th*e  crystals  can 
of  course  vary  in  the  most  manifold  way.  The  actual  shape  of  a 
body  is  therefore  not  determined  by  its  crystalline  properties,  and 
these  only  determine  certain  definite  relations  between  the  surfaces 
of  the  infinitely  varied  forms  in  which  a  substance  can  appear. 


28  FUNDAMENTAL  PRINCIPLES   OF  CHEMISTRY 

Groups  of  crystals  of  the  same  substance  are  often  found  in 
nature.  If  the  individual  crystals  which  make  up  such  a  cluster 
are  compared,  each  will  be  found  different  from  every  other  one ; 
but  in  spite  of  this  the  agreement  in  the  angle  at  which  surfaces 
meet  shows  a  certain  similarity  in  the  individual  crystals,  which 
is  so  evident  that  a  crystallographer  can,  at  the  first  glance,  recog- 
nise the  same  crystal  form  in  all  these  individual  crystals. 

All  solid  bodies  do  not  have  crystal  form.  Some,  like  glass, 
rosin,  melted  sugar,  and  so  forth,  have  none,  and  these  are  called 
amorphous  (shapeless)  bodies.  They  may  be  recognised  by  the 
fact  that  plane  surfaces,  cutting  each  other  at  a  definite  constant 
angle,  never  naturally  form  on  them.  Their  bounding  surfaces 
are  usually  curved,  and  if  they  are  broken  they  show  a  curved 
fracture.  Crystals,  on  the  other  hand,  usually  show  plane  sur- 
faces where  they  are  broken,  and  these  surfaces  are  parallel  to 
some  of  their  natural  plane  bounding  surfaces. 

There  is  another  important  difference  between  crystals  and 
amorphous  bodies.  In  all  crystals  properties  which  are  connected 
show  direction  with  different  values  in  the  same  body  when  they 
are  measured  in  different  directions.  Elasticity,  hardness,  refrac- 
tion, often  even  colour,  may  vary  in  different  directions  in  a  crystal. 
This  is  not  true  of  amorphous  solid  bodies,  for  their  properties 
show  the  same  values  in  all  directions. 

20.  ELASTICITY  AND  ENERGY  OF  SHAPE.  —  It  has  been  said 
that  solid  bodies  retain  their  shape,  and  if  we  inquire  into  this  more 
closely  we  find  that  work  or  mechanical  energy  must  be  used  to 
make  them  change  their  shape.  As  long  as  work  is  not  expended 
on  them  their  shape  remains  unchanged.  We  are  dealing  then 
with  a  special  kind  of  mechanical  energy,  which  is  called  elasticity 
or  energy  of  shape. 

The  work  which  is  expended  in  changing  the  shape  of  a  solid 
body  may  be  used  up  in  two  different  ways.  After  the  body  has 
been  acted  upon,  for  example,  after  it  has  been  bent,  it  may  take 
on  its  original  form  again.  Under  these  circumstances  it  gives 


THE  THREE  STATES  29 

back  the  work  expended  on  it,  just  as  a  clock  spring  once  wound 
up  drives  the  mechanism  of  the  clock  while  it  is  unwinding.  Such 
a  body  is  said  to  be  elastic.  It  can  take  in  energy  of  shape  and 
give  it  out  again  and  the  quantity  of  energy  taken  in  is,  in  general, 
proportional  to  the  change  of  form.  On  the  other  hand,  the  body 
may  continue  in  its  new  shape  after  work  has  been  expended  on 
it.  This  work  has  apparently  disappeared,  for  the  body  does  not 
give  it  up  again  by  changing  back  to  its  original  form,  and  it  will 
in  fact  be  necessary  to  expend  more  work  to  get  it  back  again.  If 
the  law  of  the  conservation  of  energy  is  true,  we  must  inquire  what 
has  become  of  the  expended  work,  and  the  answer  is  that  it  has 
been  transformed  into  heat.  This  can  be  shown,  for  example,  by 
bending  a  stick  of  tin  repeatedly  back  and  forth  at  the  same  place. 
It  soon  becomes  noticeably  warm.  Such  bodies  are  said  to  be 
inelastic,  and  the  property  which  results  in  changing  work  into 
heat  within  them  is  called  their  viscosity.  We  shall  find  this  same 
property  again  in  liquids,  but  it  is  very  much  greater  in  solid  bodies. 

Both  these  properties  are  always  present  in  every  solid  body,  but 
in  very  different  proportions.  Some  metals,  like  steel,  can  absorb 
large  amounts  of  energy  of  shape.  They  can  be  greatly  deformed, 
and  still  give  up  the  work  used  in  deforming  them  at  the  same 
time  that  they  assume  their  original  form.  Other  bodies  can 
change  their  shape  only  very  slightly,  and  if  one  of  these  is  de- 
formed too  far,  energy  of  shape  is  transformed  into  heat.  The 
limit  which  separates  these  two  regions  is  called  the  elastic  limit. 
Even  the  most  perfect  elastic  bodies  have  an  elastic  limit,  and 
change  their  shape  when  it  is  exceeded.  In  the  same  way  ap- 
parently inelastic  bodies,  like  lead,  possess  elasticity  within  very 
narrow  limits. 

21.  SURFACE  ENERGY.  If  a  change  in  shape  is  carried  still 
further,  a  new  phenomenon  appears.  The  body  in  question 
breaks  or  tears.  This  happens  in  any  given  case  the  more  easily 
as  the  change  of  shape  is  made  more  rapidly.  The  most  impor- 
tant point  here  is  that  new  surfaces  are  formed.  These  are  the 


30  FUNDAMENTAL   PRINCIPLES   OF  CHEMISTRY 

centre  of  another  kind  of  energy  called  surface  energy.  A  break 
or  tear  can  be  expressed  as  the  mechanical  expenditure  of  work 
which  leads  to  the  production  of  surface  energy.  A  larger  or 
smaller  portion  of  the  expended  energy  is  usually  transformed 
into  heat,  and  an  efficient  machine  for  pulverizing  bodies  means 
one  in  which  the  fraction  of  expended  energy  which  is  trans- 
formed into  heat  is  small.  We  shall  consider  surface  energy  more 
minutely  when  we  come  to  liquids.  It  is  better  to  consider  it  at 
that  point,  because  the  production  of  new  surfaces  in  solid  bodies 
is  always  connected  with  a  change  in  several  forms  of  energy,  and 
it  is  difficult  to  separate  and  determine  the  part  which  belongs  to 
surface  energy. 

22.  CHANGE  OF  VOLUME  IN  SOLIDS.  —  The  influence  of 
pressure  and  temperature  on  the  volume  of  solid  bodies  is  very 
slight.  The  compressibility  of  solids  is  so  small  that  it  escaped 
measurement  for  a  long  time,  and  it  can  only  be  measured  with 
difficulty  at  the  present  time.  The  expansion  of  solids  under  the 
influence  of  a  change  in  temperature  is  somewhat  greater,  and 
many  of  the  phenomena  of  daily  life  depend  upon  the  fact  that 
such  bodies  have  a  larger  volume  at  high  temperatures  than  at 
low  ones.  A  glass  stopper  which  is  stuck  in  a  bottle  can  be  loosened 
by  heating  the  neck  of  the  bottle.  This  expands  before  the  stopper 
itself  becomes  warm,  and  the  latter  can  then  be  removed.  The 
numerical  value  of  the  coefficient  of  expansion  depends  very 
largely  on  the  nature  of  the  substance  itself,  but  does  not  change 
very  much  with-  temperature.  The  following  table  gives  the  co- 
efficients of  expansion  of  some  substances  at  ordinary  temperature ; 
that  is,  at  18°.  They  indicate,  according  to  our  definition,  the 
fraction  of  the  volume  which  the  volume  changes  for  a  change 
in  temperature  of  one  degree. 


THE  THREE   STATES  31 

COEFFICIENTS  OF  EXPANSION  AT  18  DEGREES 

Lead 0.000083 

Aluminium ,.   .    .    .  0.000065 

Silver 0.000055 

Copper    . 0.000048 

Gold 0.000041 

Steel 0.000030 

Platinum-Iridium      . .~ 0.000026 

Glass 0.00002-0.00003 

Quartz,  melted 0.0000012 

The  coefficient  of  linear  expansion  of  a  body  is  different  from 
that  for  cubic  expansion.  It  is  the  increase  of  length  brought 
about  in  the  unit  of  length  for  a  rise  in  temperature  of  one  degree. 
It  may  be  calculated  with  sufficient  accuracy  by  dividing  the  co- 
efficient of  cubic  expansion  by  three. 

There  are  a  few  solid  bodies  which  behave  in  quite  a  different 
way,  decreasing  their  volume  with  a  rise  of  temperature,  but  none 
of  the  more  common  substances  show  this  property. 

23.  EXPANSION  OF  CRYSTALS.  —  In  the  general  increase  of 
volume  which  takes  place  during  expansion  every  dimension  of 
a  body  of  any  shape  whatever  is  changed.  If  the  substance 
is  amorphous  all  these  expansions  are  proportional  to  the  dimen- 
sions, so  that  the  geometric  shape  remains  the  same  at  various 
temperatures. 

In  the  case  of  crystals  this  is  no  longer  generally  true.  They 
expand  differently  in  different  directions,  and  there  are  in  fact 
crystals  which  expand  in  certain  directions  on  being  heated  and 
contract  in  other  directions.  But  these  changes  always  take  place 
in  such  a  way  that  straight  lines  in  the  crystals  remain  straight 
and  planes  remain  planes. 

If  spheres  are  cut  out  of  various  crystals  and  subjected  to  change 
of  temperature,  only  those  from  certain  crystals  remain  spheres, 
and  these,  of  course,  show  a  change  in  radius.  Others  lose  this 
spherical  shape  and  change  into  uniaxial  or  triaxial  ellipsoids. 


32  FUNDAMENTAL   PRINCIPLES  OF  CHEMISTRY 

Uniaxial  ellipsoids  are  egg-shaped  or  flattened  bodies  which  are 
formed  by  the  rotation  of  an  ellipse  about  one  of  its  axes.  Triaxial 
ellipsoids  are  produced  when  the  ellipse  changes  during  the  rota- 
tion about  one  of  its  axes,  becoming  narrowed  or  flattened  in 
such  a  way  that  its  points  no  longer  describe  circles  but  similar 
ellipses.  A  section  of  a  uniaxial  ellipsoid,  cut  perpendicular  to 
the  axis  of  rotation,  is  a  circle.  A  similar  section  of  a  triaxial 
ellipsoid  is  an  ellipse. 

These  facts  determine  the  division  of  all  crystals  into  three 
principal  groups :  regular,  uniaxial,  and  triaxial. 

A  crystal  behaves  in  a  precisely  similar  way  when  its  volume  is 
changed  by  a  change  of  pressure  instead  of  by  heating  or  cooling 
it.  In  this  case  also  spheres  either  remain  spheres  or  else  change 
into  uniaxial  or  triaxial  ellipsoids.  Expansion  under  the  influence 
of  heat  and  compressibility  may  therefore,  either  of  them,  be  used 
as  indication  of  the  classes  to  which  various  crystals  belong.  But 
not  very  much  is  known  about  the  compressibility  of  crystals  be- 
cause of  its  exceedingly  small  numerical  value. 

Other  properties,  the  velocity  of  light  and  heat  conductivity, 
for  example,  show  similar  differences  in  different  crystals.  Here 
experience  has  shown  the  general  law  that  a  crystal  may  be  classi- 
fied with  perfect  definiteness  by  the  investigation  of  any  one  of 
these  properties. 

24.  LIQUIDS.  —  Liquid  bodies  differ  from  solids  in  having  no 
shape  of  their  own.    They  take  on  any  shape  which  may  be  im- 
pressed upon  them  by  external  causes.     When  a  liquid  is  poured 
into  a  vessel  its  shape  is  determined  by  the  bottom  of  the  vessel 
below,  and  at  its  surface  by  the  force  of  gravity,  under  the  in- 
fluence of  which  it  sinks  as  deeply  as  possible.    The  result  is  that  a 
liquid  fills  the  lower  part  of  a  vessel  completely,  while  it  is  bounded 
above  by  a  plane  perpendicular  to  the  direction  of  gravity. 

25.  SURFACE  ENERGY.  —  A  kind  of  energy  is  active  at  the  sur- 
face of  every  liquid,  tending  to  make  this  surface  as  small  as  pos- 
sible.   It  is  called  surface  energy,  and  its  intensity  factor  is  surface 


THE  THREE  STATES  33 

tension.  Under  its  influence  falling  drops  of  rain  take  on  the 
shape  of  spheres,  because  the  sphere  has,  among  all  geometrical 
forms,  the  smallest  surface  and  the  greatest  volume.  Small  drops 
of  mercury  also  take  on  a  spherical  shape,  the  effect  of  surface 
tension  outweighing  that  of  gravity.  The  larger  the  drops  the 
more  evident  the  effect  of  gravity,  and  larger  drops  are  always 
flatter  in  shape  than  small  ones. 

When  a  liquid  is  bounded  by  a  gas  its  surface  tension  is  always 
evident  in  the  sense  just  mentioned.  If  a  liquid  is  bounded  by  a 
solid  two  cases  are  possible,  —  a  surface  tension  in  the  same  sense 
as  in  the  case  of  the  gaseous  bounding  medium  may  appear,  or 
we  may  have  a  surface  tension  of  opposite  character.  In  this  case 
the  surface  does  not  tend  to  become  as  small  as  possible,  but  as 
large  as  possible,  and  we  say  that  the  solid  body  is  wet  by  the 
liquid.  Mercury  on  glass  is  an  example  of  the  first  case;  oil  on 
glass,  of  the  second.  For  this  reason  a  drop  of  mercury  on  a  glass 
surface  assumes  a  shape  approximately  spherical,  while  a  drop 
of  oil  on  glass  spreads  out  and  appears  to  form  a  contact  surface 
as  large  as  possible.  The  majority  of  liquids  and  solids  corre- 
spond to  the  second  case,  that  is  to  say,  most  liquids  wet  most 
solid  bodies.  When  the  surface  of  a  solid  is  wet  by  a  liquid,  it 
acts  like  a  surface  of  liquid,  and  therefore  apparently  seeks  to  be- 
come as  small  as  possible.  The  rise  of  liquids  in  tubes  is  an  ex- 
ample, and  for  the  same  reason  the  edge  where  a  liquid  comes  in 
contact  with  the  wall  of  a  containing  vessel  always  curves  upwards. 
The  surface  of  a  liquid  which  wets  the  containing  vessel  is  there- 
fore really  only  plane  at  the  centre.  Near  the  edge  the  surface 
takes  on  a  dished  appearance,  and  when  the  vessel  is  only  a  centi- 
metre wide  or  less  the  whole  surface  of  a  liquid  is  curved. 

26.  VISCOSITY.  —  The  tendency  of  liquids  to  assume  any  shape 
which  is  impressed  upon  them  by  external  forces  indicates  that  it 
does  not  require  the  expenditure  of  work  to  change  the  shape  of 
a  liquid  (it  being  understood  that  no  work  is  expended  in  other 
ways,  as,  for  example,  against  gravity).  This  is  the  definition  of 
3 


34  FUNDAMENTAL   PRINCIPLES  OF  CHEMISTRY 

an  ideal  liquid,  and  all  real  ones  deviate  more  or  less  from  it.  As 
a  matter  of  fact  the  expenditure  of  work  is  always  necessary  to 
move  the  parts  of  a  liquid  about  each  other,  and  this  work  is 
different  in  amount  in  different  liquids.  In  ether  and  warm 
water  it  is  comparatively  small;  in  molasses  it  is  large.  This 
property,  which  is  a  measure  of  the  work  done  during  the  mutual 
motion  of  the  parts  of  a  liquid,  is  called  the  viscosity  of  the 
liquid,  and  it  is  small  in  ether  and  warm  water,  and  large  in 
molasses. 

As  the  viscosity  of  a  body  becomes  greater  and  greater,  it  changes 
from  a  liquid  to  a  solid.  This  is  evident  in  wax,  for  example, 
which  acts  like  a  viscous  liquid  when  it  is  warm,  and  like  a  glassy, 
brittle  solid  when  it  is  cold.  Glass  is  a  viscous  liquid  at  high 
temperatures,  and  when  it  is  cooled  it  passes  continuously  from 
this  condition  into  that  of  a  solid.  The  solid  bodies  which  are  pro- 
duced from  liquids  in  this  way  are  always  amorphous  (Sec.  19), 
and  amorphous  solids  soften  on  heating  and  change  continuously 
into  liquids,  which  are  at  first  very  viscous  indeed,  but  which  lose 
their  viscosity  gradually  on  a  further  increase  in  temperature. 

27.  VOLUME.  —  Although  liquids  have  no  shape  of  their  own, 
they  do  have  a  definite  volume.  This  does  not  mean  that  they 
cannot  change  in  volume,  but  only  that  the  volume  has  a  definite 
value  under  definite  conditions  of  pressure  and  temperature,  and 
that  it  changes  by  only  a  comparatively  small  amount  wTith  a 
change  in  these  two  conditions.  If  we  could  double  the  pressure 
which  is  exerted  on  all  bodies  on  the  surface  of  the  earth  by  the 
column  of  air  above  them,  the  volume  occupied  by  water  would 
only  be  decreased  one  forty-three  millionth  part  of  the  total  volume. 
An  increase  of  pressure  of  one  atmosphere  would  therefore  decrease 
the  volume  of  a  litre  of  water  by  only  43  cubic  millimetres.  The 
change  in  volume  is  so  small  that  accurate  apparatus  is  necessary 
to  demonstrate  and  measure  it. 

Liquids  in  general  act  very  much  like  water  in  this  respect, 
but  most  of  them  can  be  more  easily  compressed.  The  various 


THE  THREE  STATES  35 

liquids  are  all  different,  however,  and  each  of  them  has  its  own 
compressibility. 

Compressibility  is  measured  (Sec.  16)  in  terms  of  the  fraction  of 
the  total  volume  by  which  the  volume  of  the  liquid  is  changed  as 
the  consequence  of  unit  change  of  pressure.  If  we  use  in  this 
calculation  unit  volume,  the  result  is  the  numerical  value  of  the 
compressibility,  and  it  is  called  the  coefficient  of  compressibility. 
The  atmosphere  is  the  ordinary  unit  of  pressure,  and  in  terms  of 
this  unit  the  compressibility  of  water,  as  above  stated,  is  0.000043. 
This  value  varies  with  temperature  and  also  with  pressure. 

The  space  occupied  by  a  liquid  changes  with  temperature,  and, 
as  a  rule,  the  volume  of  a  liquid  increases  with  increasing  tempera- 
ture. Equal  volumes  of  various  liquids  expand  by  very  different 
amounts  under  the  influence  of  the  same  increase  in  temperature. 
The  expansibility  of  a  liquid  is  therefore  a  specific  property  of  a 
liquid,  just  as  its  compressibility  is.  It  is  expressed  by  the  frac- 
tion of  the  volume  at  0°  which  the  liquid  expands  for  a  rise  of 
temperature  of  one  degree.  This  fraction  changes,  in  general, 
with  the  temperature,  the  expansibility  becoming  greater  and 
greater  as  the  temperature  rises.  Mercury  is  somewhat  of  an  ex- 
ception, for  between  0°  and  100°  it  expands  nearly  proportional 
to  the  gases,  and  since  the  expansibility  of  a  gas  is  the  basis  of 
temperature  measurements,  the  expansibility  of  mercury  can  also 
be  used  for  this  purpose.  The  mercury  thermometer  is  an  instru- 
ment based  on  this  property.  It  consists  of  a  vessel  filled  with 
mercury  connected  with  a  fine  capillary  tube.  When  the  mercury 
changes  its  volume  with  change  of  temperature,  the  column  in 
the  tube  changes  its  length,  and  its  position  can  be  read  on  a  scale 
placed  close  to  the  mercury  column.  The  volume  of  mercury 
increases  by  0.0181  for  a  change  of  temperature  from  0°  to  100°. 
Its  coefficient  of  expansion  is  therefore  0.000181. 

As  a  matter  of  fact  what  one  observes  in  a  thermometer  is  not 
alone  the  expansion  of  mercury,  but  the  difference  between  the 
expansion  of  the  mercury  and  that  of  the  glass  vessel  in  which  it  is 


36  FUNDAMENTAL  PRINCIPLES  OF  CHEMISTRY 

inclosed.  The  expansibility  of  glass  is  very  much  smaller  than 
that  of  mercury  and  so  the  latter  rises  in  the  tube  when  the  tem- 
perature Arises.  If,  however,  the  expansibility  of  glass  were  greater 
than  that  of  mercury,  the  mercury  would  fall  in  a  thermometer  as 
the  temperature  increased,  and  if  the  two  expansibilities  were 
equal,  there  would  be  no  change  in  the  reading  of  the  thermometer 
when  the  temperature  changed. 

28.  WATER  AN  EXCEPTION.  —  There  is  an  important  excep- 
tion to  the  rule  that  the  volume  of  a  liquid  increases  with  increase 
of  temperature.  In  place  of  expanding  between  0°  and  4°,  water 
contracts.  It  has  its  least  volume  at  4°,  and  when  the  temperature 
rises  above  this  point,  it  acts  like  the  other  liquids,  its  volume  in- 
creasing with  rising  temperature.  In  winter,  when  the  tempera- 
ture is  below  zero,  ponds  and  lakes  cool  down  only  as  far  as  4°. 
The  water  at  the  surface,  which  is  cooled  by  contact  with  cold  air, 
or  by  radiation,  sinks  to  the  bottom,  since  it  is  heavier  than  the 
warmer  water.  When  a  temperature  of  4°  is  reached  through  the 
whole  body,  the  water  at  the  surface  cools  still  further;  but  it  is 
now  lighter  than  the  water  in  the  main  body  of  the  pond,  and  re- 
mains on  the  top  until  it  finally  begins  to  freeze.  The  ice  which 
forms  is  also  lighter  than  liquid  water,  and  therefore  remains 
floating  on  the  surface.  This  is  the  reason  why  still  bodies  of  water 
do  not  freeze  solid  in  winter. 

If  a  glass  vessel  like  a  thermometer  is  filled  with  water  and  sub- 
jected to  changes  of  temperature,  it  will  be  found  that  the  column 
of  water  in  the  tube  does  not  show  a  minimum  height  at  4°,  but 
at  about  8°.  What  we  observe  in  such  an  apparatus  is  the  difference 
between  the  expansibility  of  the  liquid  and  that  of  the  vessel.  If 
the  temperature  is  raised  from  4°  to  5°,  the  water  expands  a  little, 
but  the  expansion  of  the  glass  vessel  outweighs  this  expansion  and 
the  column  of  water  in  the  tube  sinks.  It  is  only  at  about  8°  that 
the  expansion  of  the  water  outweighs  that  of  glass,  and  from  this 
point  on  the  column  of  water  rises  with  a  rising  temperature. 

The  density  and  the  specific  volume  of  water  are  necessary  in 


THE  THREE   STATES 


37 


many  measurements  and  calculations.    A  table  of  their  values  is 
therefore  appended. 


Temper- 
ature. 

Specific 
Volume. 

Density. 

Tempera- 
ture. 

Specific 
Volume. 

Density. 

0° 

1.000132 

0.999868 

15° 

1.000874 

0.999126 

1° 

1.000073 

0.999927 

16° 

1.001031 

0.998970 

2° 

1.000032 

0.999968 

17° 

1.001200 

0.998801 

3° 

1.000008 

0.999992 

18° 

1.001380 

0.998622 

4° 

1.000000 

1.000000 

19° 

1.001571 

0.998432 

5° 

1.000008 

0.999992 

20° 

1.001773 

0.998230 

6° 

1.000032 

0.999968 

30° 

1.00435 

0.99567 

7° 

1.000071 

0.999929 

40° 

1.00782 

0.99224 

8° 

1.000124 

0.999876 

50° 

1.01207 

0.98807 

9° 

1.000192 

0.999808 

60° 

1.01705 

0.98324 

10° 

1.000273 

0.999727 

70° 

1.02270 

0.97781 

11° 

1.000368 

0.999632 

80° 

1.02899 

0.97183 

12° 

1.000476 

0.999525 

90° 

1.03590 

0.95838 

13° 

1.000596 

0.999404 

100° 

1.04343 

0.95838 

14° 

1.000729 

0.999271 

29.  MEASUREMENT  OF  DENSITY.  —  It  is  very  much  easier  to 
measure  the  density  and  the  specific  volume  of  liquids  than  it  is 
to  measure  them  in  solids,  and  it  is  usual  to  base  the  determina- 
tion of  these  properties  in  solids  on  a  previous  determination  of 
their  value  in  a  liquid.  Liquids  fill  easily  and  completely  any  space 
which  is  offered  to  them.  Their  volume  can  therefore  be  very 
conveniently  determined,  while  the  determination  of  the  volume 
of  solids,  especially  those  with  irregular  shapes,  is  much  more  diffi- 
cult to  carry  out.  The  simplest  method  consists  in  filling  a  vessel 
of  known  volume  with  a  liquid  and  determining  its  weight.  This 

W  V 

gives  us  both  V  and  W,  and  we  can  calculate  d  =  —  and  v  =  — . 

The  vessel  used  for  this  purpose  may  be  either  a  flask  with  a  long 
neck,  provided  with  a  mark  half  way  up  the  neck,  or  a  flask  whose 
volume  is  fixed  by  a  ground  stopper.  The  weight  of  the  empty 
flask,  its  "  tare,"  as  it  is  called,  and  its  volume  are  determined 
once  for  all,  and  it  is  then  only  necessary  to  determine  the  weight 


38  FUNDAMENTAL   PRINCIPLES   OF  CHEMISTRY 

of  the  flask  filled  with  a  liquid,  in  order  to  obtain  the  numerical 
value  for  its  density  and  specific  volume. 

The  volume  of  the  flask  is  determined  by  weighing  it  after  it 
has  been  filled  with  a  liquid  of  known  density.  This  weight 
divided  by  the  density  gives  the  volume.  Water  is  the  liquid 
usually  chosen  for  this  purpose,  for  its  weight,  when  taken  at  4°, 
gives  the  numerical  value  of  its  volume. 

Labour  is  saved  by  making  the  volume  of  the  vessel  a  round 
number  of  cubic  centimetres,  1  or  10  or  100,  for  example.  In  the 
first  case  the  weight  of  the  liquid  gives  the  density  directly.  In 
the  other  case  one  needs  only  to  point  off  the  right  number  of 
decimal  places  to  obtain  the  density. 

In  every  determination  of  weight  it  must  be  remembered  that 
the  air  introduces  an  additional  factor  because  of  its  buoyant 
effect,  and  this  must  always  be  taken  into  account. 

Another  very  common  method  of  determining  the  density  of 
liquids  consists  in  floating  a  vessel  with  a  long  cylindrical  neck 
in  the  liquid,  and  observing  the  point  to  which  it  sinks.  Accord- 
ing to  Archimedes'  principle  such  a  float  sinks  until  the  displaced 
liquid  weighs  as  much  as  the  float  itself.  The  first  method  enables 
us  to  compare  the  weight  of  equal  volumes,  the  second  method,  the 
volume  of  equal  weights ;  for  the  reading  on  the  neck  of  the  float, 
or  hydrometer,  as  it  is  called,  gives  the  volume  occupied  by  an 
amount  of  liquid  of  the  same  weight  as  the  hydrometer.  If  the 
divisions  on  the  neck  are  made  in  terms  of  the  total  volume  of  the 
hydrometer,  the  specific  volume  of  the  liquid  may  be  read  off 
directly,  just  as  densities  were  directly  obtained  in  the  first  case. 
It  is  possible  to  obtain  densities  directly  by  an  application  of 
Archimedes'  principle.  For  this  purpose  a  body  is  so  arranged 
that  it  sinks  in  the  liquid  and  thus  always  displaces  equal  volumes. 
The  buoyant  force  on  this  sinker  is  then  determined,  that  is,  how 
much  less  it  weighs  in  the  liquid  than  in  air.  This  buoyant  force 
is  equal  to  the  weight  of  liquid  displaced,  and  the  volume  of  liquid 
displaced  is  equal  to  the  volume  of  the  sinker.  If  the  sinker  has 


THE  THREE   STATES  39 

a  volume  expressed  by  a  round  number  of  cubic  centimetres,  its 
loss  in  weight  gives  the  density  of  the  liquid. 

The  measurement  is  carried  out  by  hanging  the  sinker  on  a 
balance  by  a  fine  thread  and  weighing  it  first  in  air  and  then  in  the 
liquid.  In  order  to  determine  its  volume,  it  is  weighed  in  water  at 
4°.  Here  its  loss  of  weight  is  equal  to  its  volume  if  the  weight  is 
calculated  in  grammes  and  the  volume  in  cubic  centimetres. 

The  methods  just  described  can  also  be  applied  to  the  determina- 
tion of  the  density  and  specific  volume  of  solid  bodies.  Using  the 
first  method,  the  flask  would  first  be  weighed  empty.  Any  amount 
of  the  solid  body  is  then  placed  in  it,  and  the  whole  is  weighed 
again.  This  gives  W ',  the  weight  of  the  solid  body.  The  flask  is 
now  filled  to  the  mark  with  water  and  weighed  again.  The  in- 
crease in  weight  is  the  weight  of  the  amount  of  water  which  fills 
that  part  of  the  volume  of  the  flask  which  is  not  occupied  by  the 
solid  body.  If  this  weight  is  now  subtracted  from  the  weight  of 
water  which  fills  the  entire  flask,  the  difference  is  the  weight  of 
water  displaced  by  the  solid  body,  and  this  is  equal  to  its  volume  V. 

When  Archimedes'  principle  is  to  be  applied  in  the  determina- 
tion of  the  density  of  solids,  this  may  best  be  done  by  hanging  the 
body  on  the  balance  by  means  of  a  hair  or  very  fine  wire,  and 
determining  its  weight  in  air  and  then  its  weight  when  submerged 
in  water.  The  first  determination  gives  W  directly;  the  second 
gives  W  minus  the  buoyant  effect,  that  is,  minus  the  weight  of 
water  displaced.  The  second  value  is  subtracted  from  the  first, 
and  the  result  is  the  weight  of  water  displaced,  which  is  equal  to 
the  volume  of  the  solid. 

30.  LIQUID  CRYSTALS.  —  In  Sec.  26  we  spoke  of  a  transition 
between  liquids  and  solids  which  was  indicated  by  the  fact  that 
the  viscosity  became  very  great,  while  at  the  same  time  a  measure- 
able  elasticity  appeared.  The  body  recovered  from  slight  deforma- 
tion when  the  deforming  force  was  removed.  Beside  this  there  is 
another  kind  of  transition  exhibiting  characteristics  which  are,  in 
some  degree,  contradictory  to  those  previously  discussed.  Solids 


40  FUNDAMENTAL   PRINCIPLES  OF  CHEMISTRY 

which  are  produced  from  liquids  continuously  are  amorphous  and 
isotropic,  but  the  bodies  which  we  are  considering  here,  although 
crystalline,  have  a  comparatively  very  small  viscosity,  and  an 
elasticity  which  is  so  small  as  to  be  almost  unmeasurable.  They 
are  therefore  called  liquid  crystals  and  crystalline  liquids.  Their 
crystalline  properties  are  especially  evidenced  by  their  optical 
peculiarities;  light  has  different  velocities  in  different  directions 
in  them,  and  this  results  in  peculiar  refraction  effects  which  are 
especially  evident  in  polarized  light.  In  other  respects  they  be- 
have like  liquids,  forming  drops  as  a  result  of  their  surface  tension. 
Liquid  crystals  show  all  degrees  of  viscosity,  and  those  which  are 
nearest  like  solids  take  on  shapes  somewhat  like  crystals.  Their 
points  and  edges  are,  however,  always  rounded  by  the  action  of 
surface  tension  and  because  of  the  soft  nature  of  the  substance. 
In  others  crystal  forms  only  appear  under  especially  favourable 
circumstances,  and  those  which  are  nearest  like  liquids  no  longer 
show  any  semblance  of  crystal  form,  appearing  merely  as  round 
drops. 

Liquid  crystals  are  rather  rare,  and  among  the  many  thousand 
different  substances  which  are  known  there  are  only  a  few  dozen 
which  form  them. 

31.  GASES.  —  Gases   differ   from   liquids   in    that   they   have 
neither  shape  nor  volume  of  their  own.    They  fill  any  space  which 
is  offered  to  them  completely,  and  not  only  partially,  like  liquids. 
A  gas  fills  any  space  which  is  offered  to  it  because  of  what  is  called 
its  pressure.    This  pressure  is  the  intensity  factor  of  volume  energy 
(Sec.  14).    No  such  property  is  present  in  solid  and  liquid  bodies. 
They  have  a  definite  volume,  and  fill  a  space  offered  to  them  only 
as  far  as  this  volume  reaches. 

32.  BOYLE'S    LAW.  —  As   the   volume   occupied   by   a   given 
amount  of  gas  becomes  greater,  its  pressure,  which  is  the  measure 
of  its  tendency  to  fill  a  greater  space,  becomes  less  and  less.    The 
relation  between  volume  and  pressure  is  of  the  simplest  form. 
These  two  factors  are  in  inverse  proportion  to  one  another,  and 


THE  THREE   STATES  41 

therefore  when  the  volume  is  increased  to  n  times  its  original 
value,  the  pressure  decreases  to  -  of  this  value.  This  is  called 

IV 

Boyle's  Law,  from  its  first  discoverer.  If  the  pressure  measured 
in  terms  of  a  definite  unit  is  designated  by  P,  Boyle's  Law  is  ex- 
pressed by  the  formula 


where  K  has  a  constant  value  which  depends  upon  the  amount 
of  gas  involved,  and  is  proportional  to  this  amount.  A  definite 
value  can  be  used  to  describe  solids  and  liquids  either  in  terms  of 
weight  or  of  volume,  since  these  two  things  are  proportional  in  the 
case  of  solids  and  liquids.  The  volumes  of  various  gases  are,  how- 
ever, only  proportional  to  the  amounts  of  gases  involved  when 
they  are  under  the  same  pressure.  Under  different  pressures  the 
weight  of  a  given  volume  of  gas  is  proportional  to  the  pressure. 
This  expresses  the  fact  that  more  and  more  of  a  gas  can  be  brought 
into  the  same  volume  as  the  pressure  is  increased.  This  is  ex- 
pressed by  the  equation  PV  =  K,  and  K  can  therefore  be  used 
as  a  measure  for  the  amount  of  gas,  i.  e.  for  its  weight. 

K  takes  on  a  definite  meaning  when  P  is  made  equal  to  1,  for 
then  V  =  K,  i.  e.  the  constant  K  is  the  volume  of  the  gas  when 
unit  pressure  is  acting  upon  it.  And  of  course  if  F  =  l,  K  repre- 
sents the  pressure  of  a  gas  which  occupies  unit  volume. 

Physicists  have  agreed  to  adopt  as  the  unit  of  pressure  the 
hydrostatic  pressure  of  a  mercury  column  76  cm.  high,  and  this 
unit  is  called  an  atmosphere,  because  it  corresponds  approximately 
to  the  average  pressure  of  the  atmosphere  on  the  earth's  surface. 
Gases  which  are  in  equilibrium  with  the  surrounding  air  exist 
under  this  pressure.  Gases  which  are  shut  off  from  the  atmos- 
phere by  water  or  mercury  exist  under  a  pressure  which  may  be 
greater  or  less  than  one  atmosphere,  depending  on  whether  the 
column  of  liquid  adds  its  pressure  to  that  of  the  atmosphere  or 
not.  In  order  to  express  the  true  pressure  under  which  the  gas 
exists  the  pressure  of  the  liquid  must  be  taken  into  account. 


42  FUNDAMENTAL   PRINCIPLES   OF  CHEMISTRY 

Since  the  density  of  mercury  is  13.6,  a  water  column  13.6  cm.  high 
is  equivalent  to  a  mercury  column  1  cm.  high  in  making  correc- 
tions of  this  kind. 

The  pressure  of  the  atmosphere  as  measured  by  the  barometer 
is  not  constant;  it  shows  variations  in  both  directions  about  its 
average  value,  and  must  therefore  be  determined  separately  every 
time  we  wish  to  measure  the  pressure  of  a  gas  which  is  not  com- 
pletely isolated  by  solid  walls  from  the  external  air.  Atmospheric 
pressure  is  measured  by  means  of  the  barometer,  which  gives 
the  value  for  this  pressure  directly  in  terms  of  centimetres  of 
mercury. 

In  the  consideration  of  Boyle's  Law  it  has  been  assumed  that 
the  temperature  remained  constant,  and  nothing  has  been  said 
about  the  value  of  this  factor.  This  tacit  assumption  is  an  ex- 
pression of  the  natural  law  that  Boyle's  Law  holds  for  any  tem- 
perature whatever.  The  pressure  or  the  volume  of  a  gas  changes 
when  its  temperature  is  changed,  but  for  each  temperature  Boyle's 
Law  holds  good. 

33.  THE  LAW  OF  GAY-LUSSAC.  —  The  fact  that  gases  change 
their  volume  with  change  of  temperature  has  just  been  mentioned. 
All  gases  show  an  increase  of  volume  (or  an  increase  in  pressure 
if  the  volume  is  kept  constant)  when  the  temperature  is  raised, 
and  all  gases  change  their  volume  in  the  same  way  under  the  in- 
fluence of  a  rise  in  temperature.  It  will  be  remembered  that  every 
solid  and  liquid  substance  has  its  own  special  coefficient  of  ex- 
pansion. Among  the  gases  this  property  is  independent  of  the 
nature  of  the  substance.  The  same  is  true  of  the  compressibility, 
for  Boyle's  Law  applies  to  all  gases  quite  independent  of  any 
differences  in  their  nature. 

If  the  volume  of  any  gas  under  a  definite  pressure  is  measured 
at  0°  (the  temperature  corresponding  to  a  mixture  of  ice  and 
water),  and  the  gas  is  then  heated  at  the  same  pressure  to  100° 
(the  temperature  of  boiling  water),  the  same  increase  in  volume 
is  observed  no  matter  what  the  nature  of  the  gas  under  investiga- 


THE  THREE   STATES  43 


tion  may  be.  The  increase  is  found  to  be  |$f  of  the  volume  at  0°, 
or,  expressed  as  a  decimal,  0.367  of  this  volume.  If  this  tempera- 
ture difference  is  divided  into  100  parts  so  that  each  part  corre- 
sponds to  the  same  increase  in  volume,  the  parts  are  then  called 
degrees,  and  the  increase  of  volume  for  each  degree  is  2Tff>  or 
0.00367  of  the  volume  at  the  freezing  point. 

34.  ABSOLUTE  TEMPERATURE  AND  THE  ABSOLUTE  ZERO.  — 
The  freezing  point  is,  of  course,  an  arbitrarily  chosen  point,  and 
temperature  can  be  measured  far  below  it.  If  degrees  of  tempera- 
ture are  so  chosen  below  the  freezing  point  that  the  change  of 
volume  for  1°  change  of  temperature  is  ^^  of  the  volume  at  the 
freezing  point,  it  is  evident  that  273  such  degrees  can  be  laid  off 
below  this  point.  At  —273°  C.  the  volume  of  the  gas  would  be 
zero,  and  if  the  temperature  could  be  decreased  below  this  point, 
the  volume  would  become  negative,  a  state  of  things  which  has  no 
meaning  whatever.  It  is  interesting  to  see  how  the  experiments 
which  have  been  made  in  low  temperatures  bear  on  this  assumption. 

As  a  matter  of  fact  investigators  have  succeeded  in  reaching  a 
point  about  10°  above  the  temperature  at  which  the  volume  of 
the  gas  would  become  zero,  i.  e.  263°  below  the  freezing  point. 
All  attempts  to  go  further  in  this  direction  have  met  with  the 
greatest  difficulties.  It  is  very  probable  that  we  will  not  be  able 
to  reach  a  much  lower  temperature,  and  we  may  therefore  take 
this  point,  273°  below  the  freezing  point,  as  the  foundation  of  our 
temperature  scale,  without  any  fear  that  negative  temperatures 
will  have  to  be  taken  into  account  in  the  future.  If  this  tempera- 
ture of  273°  C.  below  the  freezing  point  is  called  zero,  the  scale 
is  termed  an  absolute  one,  and  if  the  same  degrees  are  used  as  in 
the  ordinary  thermometric  scale,  the  freezing  point  of  water  lies 
at  273°  and  the  boiling  point  of  water  at  373°.  In  other  words, 
degrees  in  the  absolute  scale  are  found  by  adding  273  to  the  cor- 
responding reading  in  the  Centigrade  scale,  or  to  express  this  in 
a  formula,  T°  =  t°  +  273  where  T°  indicates  absolute  degrees 
and  t°  indicates  degrees  on  the  Centigrade  scale.  Absolute  tern- 


44  FUNDAMENTAL  PRINCIPLES  OF   CHEMISTRY 

peratures  are  sometimes  designated  by  A.,  just  as  Centigrade  tem- 
peratures are  followed  by  C. 

This  method  of  expressing  temperature  is  often  of  great  scientific 
advantage,  but  we  will  be  able  to  consider  at  this  point  only  one 
of  the  advantages  resulting  from  its  use.  This  is  the  great  sim- 
plicity which  is  given  to  the  expression  for  the  behaviour  of  gases 
as  affected  by  changes  in  temperature. 

If  VQ  represents  the  volume  of  a  gas  at  the  freezing  point  of 
water  and  Vt  its  volume  at  the  temperature  t°  C.,  the  latter  volume 

is  greater  than  the  volume  at  0°  C.  by  ^      of  the  latter  volume. 


°r 


Expressed  in  a  formula, 

+  273J- 


If,  however,  we  calculate  temperature  from  the  point  where  the 
volume  of  the  gas  would  be  zero,  its  volume  is  simply  proportional 
to  the  numerical  value  of  the  absolute  temperature.  Expressed 
in  a  formula,  VT  =  rT  where  VT  is  the  volume  at  the  absolute 
temperature  T,  and  r  is  the  volume  at  the  absolute  temperature  1. 

It  has  already  been  stated  that  the  absolute  zero,  which  is  273° 
lower  than  the  freezing  point  of  water,  has  never  been  attained. 
The  question  therefore  arises  how  we  have  determined  r.  The 
answer  to  this  question  is  evident  if  the  equation  VT  =  rT  is  trans- 
formed into  r  =  -~.  The  volume  is  simply  observed  at  any  tem- 
perature T°  and  divided  by  the  value  of  this  temperature  in  terms 
of  the  absolute  scale.  If,  for  example,  the  volume  is  observed 
at  the  ice  point,  it  is  to  be  divided  by  the  absolute  temperature  of 
the  ice  point,  which  is  273. 

The  expression  for  the  influence  of  temperature  on  the  volume 
of  a  gas  now  takes  on  a  form  which  is  analogous  to  the  expression 
for  the  pressure.  We  have  obtained  for  each  temperature  the 


THE  THREE  STATES  45 

y 

expression   —  =  r  where  r  is  constant.     And  just  as  in  Sec.   32 

the  constant  corresponds  to  the  volume  under  unit  pressure,  here 
the  constant  indicates  the  volume  at  temperature  1.  If  we  consider 
a  given  amount  of  gas  at  the  absolute  temperatures  7\  and  T2,  we 

V  V  V       V 

have    r  =  ^  and  r  =  — .      It   follows  directly  that  -=~  =  •=*•  or 

v        T     *i  l*  *i       ** 

~  =  -=*.     The  volumes  occupied  by  a  definite  quantity  of  gas  at 

Kj  J-  2 

different  temperatures  (the  pressure  remaining  the  same)  are  in 
the  same  proportion  as  the  temperatures  on  the  absolute  scale. 

In  all  of  this  we  have  assumed  that  the  pressure  may  have  any 
value  whatever,  provided  it  remains  unchanged.  This  involves 
the  supposition  that  the  same  change  of  volume  results  from  a 
given  change  of  temperature  whatever  the  pressure  may  be  under 
which  the  experiment  is  made.  This  assumption  is  justified,  as 
experiment  has  shown  and  as  the  following  consideration  also 
proves.  Suppose  we  have  determined  the  expansion  under  the 
pressure  1.  If  we  now  double  the  pressure  at  both  temperatures, 
the  volume  will  be  by  Boyle's  Law  one  half  of  the  previous  volume 
in  each  case.  The  relation  between  the  volumes  remains  the  same, 
for  when  both  members  of  a  proportion  are  multiplied  by  the 
same  factor  the  proportion  remains  unchanged.  The  law  of  ex- 
pansion for  gases  expresses  a  proportion  between  the  volumes  at 
various  temperatures,  and  says  nothing  about  the  absolute  values 
of  the  volumes. 

35.  THE  GAS  LAW.  One  more  question  remains  to  be  an- 
swered. How  does  the  volume  of  a  gas  change  with  a  change  in 
both  temperature  and  pressure? 

In  the  formula  for  constant  temperature  (Sec.  32),  PV  =  K,  K 
indicates  the  volume  under  a  pressure  of  one  atmosphere.  This 
formula  holds  for  all  temperatures,  for  Boyle's  Law  is  independent 
of  temperature.  Suppose  the  temperature  is  T,  then  K  is  the 
volume  under  unit  pressure  and  at  temperature  T.  This  volume, 


46  FUNDAMENTAL  PRINCIPLES  OF  CHEMISTRY 

however,  varies  according  to  the  formula  K  =  rT  (Sec.  34),  and 
if  this  value  for  K  is  substituted  in  the  previous  equation  the  re- 
sult is  PV  =  rT.  P,  V,  and  T  here  represent  any  values  whatever 
of  pressure,  volume,  and  temperature,  while  r  corresponds  to  the 
volume  at  temperature  1  and  pressure  1.  The  values  for  pres- 
sure, volume,  and  temperature  are  therefore  variable  while  r  is 
constant  for  a  given  quantity  of  gas.  r  is  therefore  a  measure  of 
a  quantity  of  a  gas  at  any  temperature  and  any  pressure,  and  its 

PV 

numerical  value    is   r  =  -=-.     This  equation   PV  =  rT    is   called 

the  gas  equation.  It  is  of  the  utmost  importance  in  physics  as 
well  as  in*ehemistry. 


CHAPTER  III 

MIXTURES,   SOLUTIONS,   AND   PURE   SUBSTANCES 

36.  STATES.  —  If  we  arrange  the  solid  bodies  which  we  find 
in  nature  or  prepare  artificially,  with  respect  to  their  specific 
properties,  the  following  facts  will  be  evident.  There  will  be  a 
large  number  of  different  bodies  possessing  the  same  specific 
properties.  Many  of  these  can  therefore  be  arranged  in  classes  in 
such  a  way  that  each  class  contains  all  the  bodies  of  the  same  spe- 
cific properties.  These  bodies  are  said  to  consist  of  the  same 
substance.  There  are,  therefore,  a  great  many  more  different 
bodies  than  there  are  different  substances.  The  possibility  of 
making  such  an  arrangement  depends,  as  we  have  already  seen, 
upon  differences  in  specific  properties.  We  will  therefore  ex- 
amine these  properties  more  closely,  and  in  doing  this  the  follow- 
ing question  immediately  arises :  Suppose  we  assume  that  we  have 
gathered  together  various  bodies,  each  of  which  possesses  one 
specific  property  which  it  exhibits  in  the  same  way,  will  the  other 
properties  then  be  different  and  will  different  classifications  re- 
sult, depending  upon  the  property  which  is  chosen  for  the  classi- 
fication ?  The  answer  to  this  question  can  be  readily  given.  We 
are,  in  general,  able  to  give  a  clear  description  of  the  different 
substances  of  which  various  bodies  consist.  It  must  therefore  be 
possible  to  classify  bodies  definitely  according  to  their  specific 
properties,  and  we  will  consider  how  this  is  to  be  done.  Certain 
properties  show  only  gross  differences  when  examined  directly. 
There  are,  for  example,  a  very  large  number  of  different  bodies 
which  are  white,  but  which  have  other  properties  differing  greatly 
from  body  to  body.  Here  one  specific  property,  white  colour,  is 

47 


48  FUNDAMENTAL   PRINCIPLES  OF  CHEMISTRY 

common  to  all  these  bodies,  while  all  the  other  properties  may  be 
different.  This  white  colour  is,  however,  definitely  connected 
with  certain  optical  properties  and  especially  with  index  of  re- 
fraction. If  the  refraction  of  these  different  white  bodies  is  meas- 
ured, it  will  be  found  that  it  is  in  general  different  in  different 
bodies,  and  if  the  bodies  are  now  classified  with  respect  to  their 
refractive  index  it  will  be  found  that  those  bodies  which  have  the 
same  index  of  refraction  will  also  show  correspondence  in  all  their 
other  properties. 

A  still  safer  method  is  to  examine  several  properties,  and  the 
general  principle  holds  true  that  if  several  specific  properties  are 
the  same  in  two  bodies,  all  other  specific  properties  will  also  be 
the  same.  The  same  classification  will  therefore  result  whichever 
one  of  these  properties  is  chosen  as  the  basis. 

That  this  special  peculiarity  is  true  of  the  bodies  which  occur 
in  nature,  or  can  be  prepared  artificially,  is  shown  by  much  of  our 
everyday  experience.  It  is  a  natural  law  that  bodies  can  be 
classified  in  such  a  way  that  all  the  specific  properties  of  a  class 
are  the  same,  no  matter  where  the  bodies  classified  may  have 
originated.  In  other  classes  other  values  of  the  specific  properties 
will  be  found. 

In  this  respect  bodies  are  like  plants  and  animals,  for  they  can 
also  be  arranged  in  classes  in  such  a  way  that  all  the  individuals 
belonging  to  a  class  show  similar  properties  different  from  those 
of  other  classes. 

The  different  classes  of  plants  and  animals  may  be  distinguished 
by  investigating  and  determining  their  properties,  and  the  various 
classes  of  bodies  can  be  characterized  by  their  properties  in  the 
same  way.  In  order  to  solve  this  problem  completely  all  the  prop- 
erties of  all  bodies  must  be  determined.  This  is  evidently  an  im- 
possible task,  but  it  is  also  an  unnecessary  one.  If  several  poplars, 
for  example,  or  several  crows  are  carefully  examined,  and  their 
properties  noted,  it  is  safe  to  conclude  that  the  same  properties 
which  have  been  observed  in  them  will  be  repeated  in  all  other 


MIXTURES,.   SOLUTIONS,   AND   PURE  SUBSTANCES         49 

poplars  and  crows.  The  justice  of  such  a  conclusion  can  be  tested 
at  any  time  and  to  any  extent  by  examining  other  members  of  the 
class  to  see  whether  or  not  the  properties  are  repeated.  In  the 
world  of  chemistry  and  physics  the  same  method  can  be  followed, 
and  results  have  shown  that  the  natural  law  given  above  holds 
true  in  every  case. 

It  is  therefore  unnecessary  to  investigate  all  the  properties  of 
all  bodies;  it  is  sufficient  to  determine  the  properties  of  one  body 
from  each  class,  and  even  this  problem  is  a  never-ending  one,  for 
new  properties  are  continually  being  recognised  and  new  bodies 
being  discovered  as  the  result  of  investigations  in  natural  science. 
Chemistry  has  for  its  problem  to  give  as  complete  a  description 
as  possible  of  the  properties  of  all  substances,  and  here,  as  in  all 
other  natural  sciences,  the  completion  of  the  task  is  an  ideal  which 
can  be  always  approached  but  never  attained. 

Natural  laws  are  of  great  assistance  in  this,  and  their  value  is 
evident  in  the  case  just  cited,  for  owing  to  our  possession  of  knowl- 
edge of  a  few  properties  we  were  able  to  recognise  the  class  in 
which  a  body  belongs,  i.  e.  we  can  predict  all  the  other  properties 
of  this  body.  We  do  not  need  to  investigate  all  bodies,  and  our 
labour  is  confined  to  the  study  of  one  body  from  each  class.  Other 
natural  laws  will  enable  us  to  make  further  predictions  and  thus 
to  spare  an  enormous  amount  of  labour.  In  spite  of  all  these  aids 
the  sphere  of  chemistry  as  well  as  that  of  any  other  science  will 
always  be  one  of  unlimited  extent. 

37.  MIXTURES.  —  Not  every  solid  body  which  we  find  in  nature 
or  prepare  artificially  agrees  with  the  description  given  above  con- 
cerning the  constancy  of  its  properties.  There  are  very  many 
cases  where  examination  with  the  eye  alone  shows  different  prop- 
erties at  different  points  on  the  same  body.  Most  of  the  natural 
rocks,  for  example,  which  make  up  the  crust  of  the  earth,  consist 
of  fragments  differing  in  colour  and  appearance.  Grayish  grains, 
reddish  prisms,  and  shining  plates  may  all  be  seen  in  the  same  bit 
of  granite. 


50  FUNDAMENTAL   PRINCIPLES   OF  CHEMISTRY 


: 


It  is,  however,  possible  to  imagine  a  piece  of  granite  to  be  broke 
up  into  such  fine  bits  that  it  is  no  longer  possible  to  see  parts  diffe 
ing  in  properties  in  the  same  fragment.  Each  fragment  consists 
of  only  one  substance.  It  would  then  be  possible  to  pick  out  all 
the  like  fragments  and  pile  them  into  a  heap.  The  result  would 
be  three  portions,  —  one  consisting  of  grayish  hard  grains,  this  is 
quartz;  another  of  reddish  prisms  of  feldspar;  and  the  third  of 
little  glistening  pieces  of  mica.  The  properties  in  each  portion 
are  now  the  same,  and  each  portion  is  therefore  called  a  substance. 
It  has  been  proven  by  means  of  this  mechanical  separation  that 
granite  is  a  mixture  of  three  different  solids,  and  we  must  there- 
fore take  into  consideration  mixtures  as  well  as  substances.  In 
cases  where  the  constituents  show  evident  differences  in  appear- 
ance, and  where  the  fragments  are  not  smaller  than  the  tenth  of 
a  millimetre,  visual  examination  is  often  sufficient  to  enable  us 
to  recognise  a  mixture.  If  the  fragments  are  smaller,  and  the 
same  assumption  of  differences  in  appearance  holds  true,  the 
microscope  enables  us  to  distinguish  parts  which  are  not  smaller 
than  the  half  of  a  light  wave,  i.  e.  about  -^-$-§-3  of  a  millimetre.  It 
is  difficult  to  distinguish  smaller  particles,  but  by  the  application 
of  strong  illumination  from  the  side  the  microscope  enables  us  to 
recognise  particles  about  100  times  smaller  than  this,  i.  e.  particles 
with  a  diameter  of  3-6  millionths  of  a  millimetre,  provided 
they  are  surrounded  by  a  transparent  medium. 

Mixtures  can  also  be  recognised  by  the  fact  that  they  diffuse 
light,  and  therefore  appear  cloudy.  Pure  substances,  on  the  other 
hand,  are  optically  homogeneous,  and  light  is  transmitted  regu- 
larly through  homogeneous  masses.  If  a  homogeneous  substance 
is  reduced  to  powder,  the  resulting  product  is  a  mixture  of  the 
substance  with  air,  and  this  mixture  appears  opaque.  If  a  solid 
body  or  a  liquid  is  cloudy,  it  may  be  concluded  with  certainty  that 
it  is  a  mixture.  Cloudy  mixtures  of  gases  have  only  a  tem- 
porary existence,  for  gases  form  homogeneous  solutions  in  all 
proportions. 


MIXTURES,   SOLUTIONS,   AND   PURE   SUBSTANCES         51 

This  means  of  recognising  mixtures  is  no  longer  a  valuable 
one  when  the  particles  become  small  in  comparison  with  the 
wave  length  of  light.  At  this  point  new  and  remarkable  phenom- 
ena appear,  in  which  the  surface  tension,  corresponding  to  the 
very  great  surface  of  separation,  begins  to  play  an  important  part. 
We  will  therefore  for  the  present  omit  them  in  this  elementary 
consideration. 

38.  METHODS  OF  SEPARATION.  —  We  have  already  made  use 
of  the  difference  in  appearance  of  the  parts  of  a  mixture  (colour, 
lustre,  etc.)  to  assist  in  a  mechanical  separation  performed  by 
hand.  This  means  that  we  made  use  of  the  properties  which  are 
evident  to  the  eye,  the  optical  properties.  If  these  are  not  suffi- 
ciently characteristic,  other  properties  may  be  used  in  the  same 
way,  provided  it  is  possible  with  their  aid  to  gather  the  different 
fragments  at  different  points  and  so  mechanically  to  separate  them. 
A  difference  in  density  can  be  made  use  of  in  this  way.  According 
to  Archimedes'  principle,  a  body  floats  on  the  surface  of  a  liquid 
denser  than  itself,  and  sinks  to  the  bottom  in  one  which  is  not  so 
dense.  If  we  drop  a  mixture  of  two  different  solids  whose  density 
is  sufficiently  different  into  a  liquid  whose  density  lies  between 
the  two,  the  denser  solid  will  drop  to  the  bottom  and  the  lighter 
one  will  rise.  In  a  short  time  the  two  substances  will  have  been 
separated,  and  they  may  be  collected  and  investigated  each  for 
itself. 

In  carrying  out  this  process  it  is  not  necessary  to  know  the 
densities  of  the  two  substances  beforehand.  If  the  mixture  is 
thrown  into  a  liquid  which  is  denser  than  either  of  the  two  sub- 
stances composing  it,  both  will  float.  If  a  second  lighter  liquid 
which  can  mix  with  the  first  in  all  proportions  is  carefully  added, 
the  liquid  will  decrease  in  density,  and  presently  a  point  will  be 
reached  where  its  density  is  less  than  that  of  one  of  the  sub- 
stances but  greater  than  that  of  the  other.  One  of  the  substances 
will  then  sink  to  the  bottom,  the  other  will  float  on  the  surface, 
and  the  separation  is  complete. 


52  FUNDAMENTAL   PRINCIPLES   OF  CHEMISTRY 

The  mixture  can  always  be  produced  again  from  its  compo- 
nents. To  be  sure  a  piece  of  granite  is  not  produced  when  the 
grains  of  quartz,  feldspar,  and  mica  resulting  from  our  separation 
are  mixed  together.  As  far  as  our  chemical  considerations  go, 
it  makes  no  difference  what  size  or  shape  the  bodies  have  which 
we  are  investigating,  and  to  a  chemist  the  mixture  of  the  three 
components  in  the  form  of  grains  is  in  no  way  different  from  the 
mineral  in  which  these  grains  were  closely  bound  together.  In 
this  sense  any  mixture  whatever  can  always  be  produced  from  its 
components,  just  as  we  can  always  separate  it  into  its  components 
by  some  means  or  other. 

39.  PROPERTIES  OF  MIXTURES.  —  Nothing  is  changed  in  the 
specific  properties  of  a  set  of  substances  when  we  bring  them  to- 
gether in  a  mixture.  The  properties  of  a  mixture  can  therefore 
be  calculated  from  the  properties  of  its  constituents  by  the  Rule 
of  Mixtures,  as  it  is  called.  If,  for  example,  one  part  of  the  mixture 
is  composed  of  x  parts  of  the  homogeneous  body  A  and  1  —  x 
parts  of  the  body  B,  and  if  a  is  the  value  for  a  specific  property  of 
the  body  A  and  b  is  the  value  for  the  corresponding  property  of 
the  body  B,  the  value  of  the  property  in  the  mixture  of  A  and  B 
will  be  ax  +  (1  —  x)b.  If  the  mixture  consists  of  three  compo- 
nents, a  similar  formula,  xa  +  yb  +  (1  —  x  —  y)c  will  be  appli- 
cable. The  word  "  parts"  must  be  taken  to  mean  parts  by 
weight  when  the  specific  property  is  based  on  the  unit  of 
weight,  and  parts  by  volume  when  it  is  based  on  the  unit  of 
volume. 

The  formula  for  mixtures  of  two  components  can  be  used  in 
two  ways.  Where  the  properties  of  the  constituents  are  known 
and  the  fraction  x,  in  which  one  constituent  is  present,  is  given 
(and  from  this  the  fraction  1  -#  of  the  other  constituent),  then  the 
value  of  the  property  in  the  mixture  can  be  calculated.  Or  x  can 
be  calculated  when  the  value  of  the  property  in  the  mixture  has 
been  determined,  by  experiment,  for  instance.  If  the  value  of 
the  property  in  the  mixture  is  called  m,  we  have  ra=  xa  +  (l—x)b, 


MIXTURES,   SOLUTIONS,   AND  PURE  SUBSTANCES         53 

or  from  this  x  =  (  -  —r  J.  This  last  formula  is  often  used  in  cal- 
culating the  constitution  of  a  mixture  of  two  bodies  from  a  meas- 
urement of  one  property.  It  can  also  be  used  in  difficult  cases  to 
determine  whether  we  have  to  do  with  a  mixture  or  not. 

In  these  cases  it  is  necessary -to  determine  the  proportions  in 
which  the  two  constituents  appear,  and  the  value  of  one  of  the 
specific  properties  of  each  constituent.  From  this  data  the  value 
of  this  same  property  in  the  suspected  mixture  is  then  to  be  cal- 
culated. If  the  calculated  value  does  not  agree  with  the  measured 
value  within  the  limit  of  error  of  the  measurements,  we  are  cer- 
tainly not  dealing  with  a  mixture.  If  it  does  agree,  it  is  very  prob- 
able that  we  are  dealing  with  a  mixture;  but  there  are  some  cases 
where  homogeneous  substances  exhibit  properties  which  agree  with 
those  calculated  from  the  Rule  of  Mixtures  as  above  described. 

40.  LIQUID  SOLUTIONS.  —  Liquids  differ  from  solid  bodies  in 
their  chemical  properties  as  well  as  in  their  mechanical  ones.  The 
Law  explained  in  Sec.  36  applies  to  solid  bodies  with  a  few  excep- 
tions which  will  be  taken  up  later,  but  the  relations  in  the  case  of 
liquids  are  much  more  complex.  Nearly  all  solid  bodies  can  be 
arranged  in  classes  in  such  a  way  that  their  properties  differ  by 
distinct  steps  from  class  to  class,  remaining  constant  within  the 
individual  class.  There  are  many  liquids  which  can  be  arranged 
in  classes  in  the  same  way  and  which  therefore  follow  the  same 
law,  but  there  are  many  more  liquids  whose  properties  can  have 
any  values  whatever  between  certain  limits.  These  intermediate 
forms  are  produced  by  mixing  two  different  liquids  in  various  pro- 
portions. In  some  cases  this  does  not  result  in  the  formation  of 
a  new  homogeneous  liquid,  but  in  many  cases  it  does.  The  liquids 
which  do  so  mix  are  said  to  dissolve  each  other,  and  the  resulting 
product  is  called  a  solution. 

These  solutions  are  just  as  homogeneous  as  the  substances  from 
which  they  are  prepared,  and  the  most  careful  optical  examination 
shows  no  trace  of  individual  constituents.  They  can  therefore  not 


54  FUNDAMENTAL  PRINCIPLES  OF  CHEMISTRY 

be  placed  in  the  same  class  with  the  mixtures  which  we  learned 
about  in  the  case  of  solid  bodies.  They  have  no  very  evident 
properties  which  distinguish  them  from  the  other  liquids  which 
obey  the  Substance  Law  of  Sec.  36.  It  is  only  when  they  are 
transformed  in  some  way  (made  to  change  their  state,  for  instance) 
that  fundamental  differences  between  them  and  the  other  class  of 
liquids  become  evident.  For  the  present  we  will  content  ourselves 
with  calling  attention  to  the  existence  of  solutions  as  distinguished 
from  substances  in  the  narrower  sense  of  the  word.  The  discus- 
sion of  the  differences  between  them  will  be  left  until  later. 

41.  SOLUTIONS  OTHER  THAN  LIQUID  ONES.  —  Solid  bodies  can 
also  form  solutions,  that  is,  they  can  form  solids  with  properties 
varying  continuously  between  certain  definite  limits.     But  such 
solutions  occur  much  less  frequently  than  in  the  case  of  liquids. 
They  occur  most  frequently  among  amorphous  substances  (Sec.  19) 
(which  can  be  regarded  as  liquids  with  very  great  viscosity)  and 
only  very  infrequently  among  crystalline  substances.     ^Tien  they 
do  occur  among  crystalline  substances,  it  is  usually  among  those 
which  are  "  isomorphous." 

With  gases  the  case  is  entirely  different.  All  gases  form  solu- 
tions with  each  other  in  all  proportions,  and  it  is  not  always  easy  to 
decide  whether  a  given  gas  is  a  solution  or  a  pure  substance.  The 
fundamental  method  of  deciding  this  point  will  be  discussed  in 
the  next  chapter. 

42.  MIXTURES    OF    LIQUIDS    WITH    SOLIDS.  —  Relations  very 
similar  to  those  given  in  the  case  of  several  solid  bodies  appear 
when  solids  are  mixed  with  liquids.     The  mixture  may  show 
properties  which  approach  those  of  one  or  other  of  its  constit- 
uents, depending  on  which  of  them  is  present  in  greater  amount. 
The  cloudy  liquids,  which  contain  only  a  small  amount  of  a  solid 
substance  in  a  large  amount  of  a  liquid,  are  to  be  considered  here. 
The  semi-liquid  and  clay-like  masses,  which  consist  of  about  equal 
parts  of  solid  and  liquid  (here  the  relative  amount  of  the  two  con- 
stituents may  vary  within  very  wide  limits),  also  belong  here. 


MIXTURES,   SOLUTIONS,   AND   PURE   SUBSTANCES         55 

Finally,  we  must  include  in  this  class  apparently  solid  masses  with 
only  a  very  small  amount  of  a  liquid  mingled  with  them. 

To  the  eye  all  of  these  are  characterized  by  their  muddiness  or 
opacity.  Only  in  those  cases  where  the  two  constituents  have  the 
same  index  of  refraction  does  this  cloudiness  disappear.  And 
even  then  it  disappears  only  when  the  mixture  is  illuminated  by 
light  of  one  particular  wave-length,  and  it  appears  again  when 
light  of  another  wave-length  is  used.  This  fact  explains  the  re- 
markable colour-phenomena  which  are  observed  in  all  of  these 
mixtures.  While  these  colour-phenomena  are  very  interesting, 
they  cannot  be  discussed  further  in  this  book. 

There  are  several  ways  of  separating  such  a  mixture,  the  most 
usual  of  which  is  filtration,  and  this  is  carried  out  by  allowing  the 
mixture  to  pass  through  a  sieve.  This  sieve  can  have  coarse  meshes 
when  the  solid  body  is  present  in  large  pieces,  but  its  meshes  must 
be  made  finer  and  finer  as  the  size  of  the  particles  to  be  separated 
decreases.  The  sieve  most  commonly  used  in  chemical  work  is 
filter  paper,  and  this  consists  of  a  thin  mass  of  hair-like  bits,  through 
whose  interstices  the  liquid  can  easily  pass  while  the  solid  particles 
are  held  back.  Paper  with  various  sizes  of  pores  must  be  used  for 
various  sizes  of  solid  particles  to  be  retained,  and  when  the  pores 
are  very  fine  the  liquid  passes  through  the  paper  slowly.  In 
general  it  is  desirable  to  finish  a  filtration  as  rapidly  as  possible, 
and  choice  must  therefore  be  made  in  each  case  of  a  paper  with 
pores  corresponding  to  the  size  of  the  solid  grains  to  be  retained. 
Gravity  is  usually  depended  on  to  carry  the  liquid  through  the 
paper,  but  the  separation  can  be  made  more  rapid  by  causing  a 
difference  of  pressure  on  the  two  sides  of  the  paper,  either  by  in- 
creasing the  pressure  above  the  liquid  in  the  filter  or  by  decreas- 
ing it  below.  In  technical  work  the  first  method  is  the  more  usual 
one,  but  in  the  laboratory  the  second  is  generally  applied. 

A  second  method  of  separation  is  based  on  the  direct  action  of 
gravity  on  such  a  mixture.  The  solid  substance  usually  has  the 
greater  density,  and  when  such  a  mixture  is  allowed  to  stand 


56  FUNDAMENTAL   PRINCIPLES  OF   CHEMISTRY 

quietly  a  separation  results,  the  solid  collecting  at  the  bottom  of 
the  containing  vessel  while  the  liquid  remains  above  in  a  pure 
state.  This  method  of  automatically  clearing  a  muddy  liquid  is 
applied  in  a  very  great  number  of  cases,  and  it  appears  everywhere 
in  natural  processes.  If  the  mixture  is  subjected  to  the  action  of 
a  centrifugal  force,  the  solid  particles,  which  have  the  greater  rela- 
tive* mass  (greater  density),  are  thrown  outward,  and  separation 
results.  The  effect  increases  as  the  square  of  the  velocity,  and 
can  therefore  be  greatly  increased  by  increasing  the  velocity.  This 
is  why  a  separation  can  be  made  much  more  quickly  and  com- 
pletely by  means  of  a  centrifuge  than  by  merely  allowing  the 
mixture  to  stand  and  settle. 

Separations  of  this  sort  are  always  incomplete,  provided  the 
solid  is  one  which  is  wet  by  the  liquid,  and  this  is  almost  invariably 
the  case.  The  liquid  comes  out  clear,  to  be  sure,  but  is  not  com- 
pletely separated,  and  the  solid  is  completely  removed,  but  not  in 
a  pure  state,  since  it  is  not  quite  free  from  the  liquid.  The  amount 
of  impurity  which  is  present  in  the  solid  after  separation  in  this 
way  can  be  reduced  as  far  as  desired  by  pressure  or  the  centrifuge, 
but  it  can  never  be  made  actually  zero. 

When  the  solid  is  present  in  larger  proportion,  masses  more  or 
less  like  dough  or  clay  are  formed,  which  act  like  liquids  with 
great  viscosity,  but  which  are  different  from  these  in  some  ways. 
The  possibility  of  forming  such  plastic  masses  into  any  shape  by 
mechanical  action  conditions  their  use  in  practical  things,  as  in 
mortar  and  clay. 

Finally,  when  the  liquid  is  present  in  very  small  amount  it 
collects  on  the  surface  of  the  solid  and  is  held  there  by  surface 
tension.  All  solid  bodies  which  have  been  lying  in  the  air  are 
covered  with  such  a  layer  of  water,  which  does  not  act  like  a  liquid 
and  cannot  be  wiped  off.  It  can  be  driven  off  by  heating  the 
body  strongly,  but  even  then  it  does  not  evaporate  as  easily  as 
ordinary  water.  Recognition  of  this  fact  is  of  importance  if  the 
weight  of  a  solid  is  to  |^e  determined.  Massive  bodies  with  a  small 


MIXTURES,   SOLUTIONS,   AND   PURE   SUBSTANCES      '57 

surface  carry  with  them  only  a  very  small  amount  of  water  in  this 
way,  but  the  amount  increases  as  the  surface  of  the  body  increases, 
and  becomes  considerable  when  we  have  to  deal  with  a  fine  powder 
or  with  thin  sheets. 

The  presence  of  this  thin  layer  may  be  made  apparent  by  the 
following  experiment :  Draw  out  a  tube  or  a  glass  rod  by  heating 
it  in  the  glass-blower's  lamp.  Break  off  the  fine  thread  so  pro- 
duced and  draw  one  piece  of  it  over  the  other.  The  freshly  formed 
surfaces  will  cling  to  each  other  in  a  very  evident  way.  But  after 
the  pieces  have  been  lying  in  the  air  for  a  time  the  surfaces  will 
glide  over  each  other  without  any  sign  of  clinging.  Clean  surfaces 
of  any  solid  will  cling  to  each  other  in  this  way,  because  solids  as 
well  as  liquids  seek  to  take  on  as  small  a  surface  as  possible,  as 
a  result  of  surface  energy.  The  thin  layer  of  water  which  forms 
in  the  air  prevents  the  surfaces  from  coming  into  contact  and 
removes  the  possibility  of  this  action. 

43.  LIQUID  MIXTURES.  —  When  two  different  liquids  are 
brought  together  they  either  form  a  homogeneous  solution  or  else 
remain  separate  (Sec.  40).  The  result  depends  very  often  on  the 
relative  amounts  of  liquid  which  are  brought  together,  for  many 
liquids  form  solutions  when  a  small  amount  of  one  is  mixed  with 
a  large  amount  of  the  other,  but  do  not  do  so  beyond  a  certain 
definite  point.  If  the  relative  amount  of  the  first  liquid  is  increased 
a  true  mixture  of  the  two  is  formed. 

Two  cases  are  here  possible.  First,  the  two  liquids  may  remain 
almost  entirely  separate.  The  less  dense  of  the  two  will  then 
float  above  the  denser  and  a  horizontal  surface  of  separation  will 
be  visible  between  them.  Second,  the  two  may  be  so  shaken  to- 
gether that  one  becomes  more  or  less  finely  divided  throughout 
the  other.  The  one  will  then  take  on  the  form  of  spherical  drops 
which  float  about  in  the  other.  In  this  case  the  conditions  men- 
tioned in  Sec.  37  will  be  found,  and  any  difference  in  the  indices 
of  refraction  of  the  two  liquids  will  cause  the  mixture  to  appear 
more  or  less  opaque.  Both  of  these  cases  may  be  seen  if  first  water 


58  FUNDAMENTAL   PRINCIPLES   OF   CHEMISTRY 

and  then  oil  be  poured  into  a  flask,  and  the  whole  afterward 
shaken.  Such  a  mixture  of  two  liquids  in  which  spherical  drops 
are  formed  is  called  an  emulsion. 

Considerations  similar  to  those  developed  for  solid-liquid  mix- 
tures in  the  previous  section  apply  to  the  separation  of  the  con- 
stituents of  liquid  mixtures.  Filtration  is  only  applicable  when 
the  liquid  which  is  to  be  held  back  can  be  prevented  from  wetting 
the  material  of  the  filter,  for  otherwise  it  will  run  through  and 
spoil  the  separation.  But  even  very  fine  emulsions  of  compo- 
nents only  slightly  differing  in  density  can  be  separated  by  the 
centrifuge.  Milk  is  a  good  example,  and  it  is  an  emulsion  of 
butter-fat  in  an  aqueous  solution  of  milk-sugar  and  casein. 

Where  the  emulsified  liquid  is  very  finely  divided  indeed,  the 
separation  becomes  much  more  difficult  on  account  of  the  effect 
of  surface  energy,  which  then  becomes  active  and  prevents  separa- 
tion in  a  way  which  we  cannot  discuss  further. 

44.  MIXTURES  OF  GASES.  —  Gases  dissolve  each  other  in  all 
proportions,  and  it  is  therefore  impossible  to  make  a  mixture  of 
two  or  more  gases.  Gases  can,  however,  form  mixtures  with 
either  liquids  or  solids.  Two  cases  are  always  to  be  considered. 
In  general,  and  because  of  surface  tension,  such  a  mixture  will 
consist  of  more  or  less  spherical  drops  of  one  of  the  bodies,  sus- 
pended throughout  a  nearly  continuous  mass  of  the  other.  De- 
pending on  whether  the  mass  or  the  suspended  portion  is  gaseous, 
the  resulting  phenomena  are  very  different. 

If  the  gas  is  the  major  mass  in  which  fine  particles  of  a  solid 
are  floating,  we  have  a  dusty  gas.  If  the  floating  particles  are 
liquid,  we  have  to  do  with  a  fog.  The  density  of  the  floating  par- 
ticles, whether  solid  or  liquid,  is  always  very  much  greater  than 
that  of  the  gas  about  them,  and  the  particles  must  therefore  be 
very  small  indeed  if  the  mixture  is  to  have  any  duration  as  such. 
For  any  given  amount  of  the  floating  body  the  resistance  to  fall 
increases  in  proportion  to  the  total  cross  section  of  the  body,  and 
this  means  that  as  the  particles  are  made  smaller  the  resistance  to 


MIXTURES,   SOLUTIONS,   AND  PURE  SUBSTANCES          59 

fall  increases  as  the  inverse  square  of  the  linear  dimensions  of  the 
particles.  In  cases  of  very  fine  division  the  resistance  is  so  great 
that  such  a  mixture  can  remain  hours  or  even  days  without  any 
apparent  separation  due  to  gravity.  In  general  it  is  easier  to  pro- 
duce a  very  fine  state  of  division  among  liquids  than  among  solids. 

45.  FOAMS.  —  In  the  other  case,  where  the  gas  forms  the  iso- 
lated particles,  the  resulting  mixture  is  called  a  Foam  (Schaum). 
This  name  is  applied  primarily  to  a  mixture  in  which  a  liquid 
forms  the  main  body  of  the  mass;  but  if  this  hardens,  a  solid 
gaseous  mixture  of  precisely  similar  structure  results,  and  the 
same  name  has  also  been  given  to  this.  Ordinary  pumice  stone 
is  just  such  a  solid  foam,  which  has  been  formed  by  the  solidifica- 
tion of  an  originally  liquid  mass  of  rock. 

Surface  energy  plays  an  important  part  here,  and  this  some- 
times results  in  great  stability  of  the  resulting  foam.  The  stability 
seems  in  general  to  be  greater  when  the  liquid  portion  is  of  a  rather 
complex  nature,  and  especially  when  it  contains  some  substances 
with  great  and  some  with  small  surface  tension.  The  foams  re- 
sulting from  pure  liquids  are  usually  very  unstable. 


CHAPTER   IV 

CHANGE   OF  STATE   AND   EQUILIBRIUM 
(a)   The  Equilibrium  Liquid  — Gas 

46.  EQUATIONS  OF  CONDITION.  —  Substances  retain  their 
properties  unchanged  only  when  the  conditions  under  which  they 
exist  remain  unchanged. 

These  conditions  may  be  of  the  most  manifold  kind,  for  all  the 
arbitrary  properties  previously  mentioned  correspond  to  differences 
in  them.  Of  all  the  possible  ones  two  are  of  especial  importance 
to  us.  These  are  temperature  and  pressure,  the  intensity  factors  of 
heat  and  volume  energy  respectively.  In  our  discussion  of  the 
various  states  in  which  bodies  may  exist  the  influence  of  these 
two  conditions  was  repeatedly  mentioned,  and  we  found  that  the 
very  first  specific  property  we  discussed,  density  or  specific  volume, 
was  influenced  in  a  quite  characteristic  way  by  both  temperature 
and  pressure.  If  a  greater  range  of  temperatures  and  pressures 
is  included,  it  is  found  that  their  influence  may  be  still  more  im- 
portant, and  that  it  may  even  determine  the  passage  of  a  substance 
from  one  state  to  another. 

If  the  behaviour  of  a  substance  is  investigated  at  various  pres- 
sures and  temperatures,  it  is  found  that  the  substance  can  be 
made  to  pass  through  a  complete  series  of  conditions  by  varying 
the  values  of  these  two  factors.  A  general  view  of  all  these  changes 
is  best  obtained  by  considering  first  the  changes  in  condition  cor- 
responding to  change  in  temperature,  the  pressure  remaining 
constant  (isobaric  changes),  and  then  those  corresponding  to  a 
change  in  pressure,  the  temperature  remaining  constant  (isother- 
mal changes). 

60 


CHANGE   OF  STATE   AND   EQUILIBRIUM  Gl 

47.  THE   LIQUEFACTION   OF   GASES.  —  Let   us  begin   with   a 
gas.     If  we  raise  its  temperature  at  constant  pressure  it  does  not 
change  its  state :   it  remains  a  gas,  merely  changing  its  volume  in 
accordance  with  the  Law  of  Gay-Lussac.     If,  however,  we  lower 
its  temperature,  we  find  a  point  where  the  gas  changes  to  a  liquid. 

This  point  may  vary,  according  to  the  nature  of  the  substance, 
between  the  widest  limits  of  our  known  temperature  scale.  Some 
gases  have  been  liquefied  only  with  the  greatest  difficulty,  because 
of  the  very  low  temperatures  necessary  for  their  liquefaction. 
These  difficulties  have  been  overcome  one  by  one,  and  now  there 
is  no  gas  known  which  has  not  been  actually  liquefied. 

The  change  of  a  gas  into  a  liquid  takes  place  suddenly,  or,  better, 
discontinuously ;  for  just  above  a  certain  definite  temperature  the 
substance  under  examination  has  all  the  properties  of  a  gas,  and 
just  below  the  same  temperature  it  has  those  of  a  liquid.  Its 
density  usually  increases  greatly,  and  all  its  other  properties  show 
a  sudden  and  usually  considerable  change.  Certain  new  proper- 
ties, surface  tension  among  them,  appear. 

In  agreement  with  our  general  definition  such  a  transformation 
is  to  be  considered  as  a  chemical  change,  for  one  substance  —  a  gas 
—  disappears  and  another  —  a  liquid  —  having  a  new  set  of  prop- 
erties appears.  It  has  been  customary  to  call  this  change  of  state 
a  physical  change,  because  it  can  be  so  easily  reversed.  But  there 
are  also  many  chemical  processes  which  can  be  just  as  easily 
reversed ;  and  beside  this,  the  general  laws,  in  accordance  with 
which  these  changes  take  place,  are  precisely  the  same  laws  as 
those  which  describe  undoubted  chemical  change.  It  is  there- 
fore better  to  consider  a  change  of  state  as  a  chemical  change  of 
the  simplest  sort. 

48.  PURE  SUBSTANCES  AND  SOLUTIONS.  —  In  changes  of  this 
type  two  separate  cases  are  to  be  distinguished,  and  their  char- 
acterization is  of  great  importance.     Either  the  whole  of  the  gas 
changes  into  a  liquid  as  liquefaction  goes  on,  without  the  tempera- 
ture being  changed  (the  pressure  remaining  constant),  or  the  tern- 


62  FUNDAMENTAL   PRINCIPLES   OF   CHEMISTRY 

perature  must  be  carried  lower  and  lower  as  liquefaction  proceeds, 
in  order  to  cause  the  remaining  portions  of  the  gas  to  liquefy. 

Gases  of  the  first  class  have  a  constant  temperature  of  lique- 
faction, and  they  are  pure  substances,  or  substances  in  the  narrower 
sense  of  the  word.  Gases  of  the  second  class  are  called  solutions. 
It  has  been  usual  to  call  gases  of  this  latter  kind  gaseous  mixtures, 
retaining  the  name  "  solution  "  for  a  certain  class  of  liquids  only.  A 
general  consideration  of  the  facts  shows  that  it  is  better  to  extend 
the  idea  solution  to  all  three  states,  and  to  consider  gaseous  and 
solid  solutions  together  with  the  liquid  ones. 

Experience  has  shown  that  a  solution  can  always  be  made  up 
from  pure  substances,  and  further,  that  it  can  always  be  broken 
up  into  the  same  pure  substances  again.  Study  of  the  pure  sub- 
stances should  therefore  precede  the  investigation  of  solutions. 
An  unlimited  number  of  solutions  can  always  be  made  up  from  the 
same  two  pure  substances,  by  giving  the  relative  amount  of  the 
constituents  any  desired  value.  Infinitely  more  solutions  than 
pure  substances  are  therefore  possible.  From  both  points  of 
view  a  knowledge  of  the  pure  substances  is  of  far  greater  im- 
portance than  a  knowledge  of  solutions,  and  we  will  devote  our- 
selves exclusively  to  them  for  the  present. 

49.  REVERSIBILITY.  —  The  phenomena  just  described  are  re- 
versible. If  the  liquid  which  has  been  obtained  by  liquefaction 
of  the  gas  is  warmed  a  little,  it  will  change  back  into  a  gas  at  the 
same  temperature  as  the  one  at  which  it  liquefied.  Gases  obtained 
in  this  way  from  liquids  are  often  called  vapours.  As  long  as  it 
was  believed  that  gases  existed  which  could  not  be  liquefied,  this 
term  had  a  definite  meaning.  At  the  present  time  the  difference  no 
longer  has  such  a  meaning,  and  the  word  "  gas  "  is  used  for  sub- 
stances in  this  state,  leaving  the  word  "  vapour  "  to  indicate  their 
relation  to  the  same  substance  in  the  liquid  and  solid  state. 

The  change  of  a  liquid  into  a  gas  (or  vapour)  is  called  vaporiza- 
tion or  boiling.  The  two  mean  the  same  in  reality,  but  it  is  usual 
to  use  the  term  "  boiling"  only  when  the  vaporization  takes  place 


CHANGE   OF  STATE   AND   EQUILIBRIUM  63 

in  such  a  way  that  bubbles  rise  through  the  liquid,  while  vaporiza- 
tion is  used  to  indicate  the  formation  of  vapour  at  the  surface  of 
the  liquid. 

Pure  substances  and  solutions  show  the  same  differences  in 
vaporization  that  they  show  in  liquefaction.  Pure  substances  go 
through  the  whole  process  at  constant  temperature,  while  solu- 
tions show  a  changing  temperature  during  the  process.  But  the 
direction  of  the  change  is  opposite  to  that  which  takes  place  during 
liquefaction.  After  vaporization  has  begun  at  a  definite  tempera- 
ture, the  temperature  must  be  raised  higher  and  higher  in  order 
to  make  the  evaporation  complete.  This  is,  of  course,  because  here 
we  are  starting  with  the  liquid  solution  and  passing  to  the  gaseous 
one,  while  in  the  other  case  we  began  with  the  gaseous  and  passed 
to  the  liquid  solution. 

This  mutual  relation  is  expressed  by  saying:  a  pure  substance 
remains  pure  independent  of  its  state,  and  a  liquid  solution  changes 
into  a  gaseous  solution,  and  vice  versa.  This  is  an  important 
conclusion. 

50.  EQUILIBRIUM.  —  A  further  conclusion  may  be  drawn  for 
pure  substances.  Such  a  substance  can  be  transformed  at  a  given 
pressure  from  one  state  to  another  at  constant  temperature.  At 
this  temperature,  therefore,  and  this  pressure  any  given  amount 
of  liquid  and  any  given  amount  of  vapour  can  exist  together  with- 
out exerting  any  influence  on  each  other.  Such  a  condition  is 
called  an  equilibrium,  and  it  has  something  in  common  with  a 
mechanical  equilibrium  in  that  it  no  longer  changes  with  time, 
provided  the  conditions  (in  this  case  pressure  and  temperature) 
do  not  change.  This  may  be  expressed  by  saying  that  under  these 
conditions  the  relative  and  absolute  amounts  of  vapour  and  liquid 
have  no  influence  on  the  equilibrium.  The  case  of  solutions  is 
different,  for  among  them  every  equilibrium  between  liquid  and 
vapour  corresponds  to  a  different  temperature. 

A  pure  substance  remains  pure  whether  it 'is  in  the  state  of 
liquid  or  in  the  state  of  vapour;-  it  is  therefore  customary  to  use  the 


64  FUNDAMENTAL   PRINCIPLES  OF  CHEMISTRY 

same  name  in  both  cases,  and  to  add  the  state  when  this  is  neces- 
sary. The  name  "  water  "  (in  the  chemical  sense)  is  used  to  desig- 
nate not  only  the  familiar  liquid,  but  also  its  vapour,  and  we 
distinguish,  when  necessary,  between  liquid  water  and  water 
vapour.  Ice  is,  of  course,  water  in  the  solid  form. 

The  transformation  of  a  pure  substance  from  one  state  to  an- 
other takes  place  under  a  given  pressure  at  constant  temperature. 
The  most  easily  observed  case  of  this  transformation  is  that  from 
liquid  to  gas  at  the  boiling  point.  If  water  is  heated  in  a  vessel 
under  ordinary  atmospheric  pressure  vapour  forms  more  and 
more  rapidly  until  100°  C.  is  reached,  and  this  temperature  con- 
tinues unchanged,  without  regard  to  the  amount  of  water  left  in 
the  vessel  or  the  amount  which  has  boiled  away,  until  all  the  water 
is  gone.  This  gives  a  means  of  producing  a  definite  temperature, 
and  use  is  made  of  this  fact  in  the  determination  of  the  funda- 
mental points  of  our  thermometric  scale.  Water  has  been  chosen 
for  this  purpose  rather  than  any  other  substance,  because  water 
is  the  easiest  to  obtain  in  the  pure  state.  Pure  substances  have 
a  constant  boiling  point,  while  the  boiling  point  of  a  solution 
changes,  increasing  as  evaporation  proceeds.  This  latter  fact  is, 
of  course,  a  characteristic  means  of  recognising  solutions. 

51.  SATURATION.  —  If  we  examine  the  condition  of  a  gas  with 
respect  to  the  possibility  of  changing  it  into  a  liquid,  by  cooling 
it  or  increasing  the  pressure  upon  it,  we  find  several  cases.  There 
is  first  of  all  a  region  of  low  pressure  and  high  temperature  where 
it  cannot  be  transformed  into  a  liquid.  This  is  called  the  unsatu^ 
rated  condition,  referring  to  saturation,  which  we  are  about  to  dis- 
cuss, and  a  vapour  in  this  region  is  called  an  unsaturated  vapour. 
If  the  pressure  is  increased  or  the  temperature  decreased  until 
liquid  can  exist  together  with  the  vapour,  the  condition  is  one  of 
saturation,  and  we  have*  to  do  with  the  saturated  vapour.  By 
saturation  we  are  therefore  to  understand,  in  general,  the  condi- 
tion of  a  phase  which  is  in  equilibrium  with  another.  We  might,  of 
course,  speak  of  a  liquid  as  saturated  with  respect  to  the  vapour ; 


CHANGE  OF  STATE  AND  EQUILIBRIUM  65 

but  this  is  not  customary,  because  the  density  of  a  liquid  usually 
varies  only  very  slightly  under  changes  of  pressure  and  tempera- 
ture, while  the  change  in  the  density  of  a  gas  under  the  same 
variation  of  conditions  is  very  great.  The  word  "saturation"  is 
therefore  used  for  those  phases  in  which  these  changes  (and  in- 
cluded with  them  changes  in  concentration)  are  easily  observed. 

If  we  go  further  with  the  lowering  of  the  temperature,  the  in- 
crease of  pressure,  or  the  increase  of  concentration,  until  the 
saturation  point  is  passed,  we  reach  the  region  of  supersaturation. 

52.  THE  INFLUENCE  OF  PRESSURE.  —  If  the  transformations 
just  described  are  investigated  at  another  pressure  the  following 
result  will  be  found  in  general.     Substances  which  have  been 
found  to  be  pure  under  one  pressure  behave,  in  general,  in  the 
same  way  under  other  pressures.     But  the  temperature  at  which 
the  transformation  takes  place  is  a  different  one  under  a  different 
pressure.     The  higher  pressure  always  corresponds  to  a  higher 
temperature.     On  the  other  hand,  substances  which  behave  like 
solutions  under  one  pressure  will  act  in   the  same  way  under 
other  pressures.     Among  solutions  also  the  temperature  at  which 
transformation  into  another  state  begins  is  higher  for  a  higher 
pressure,  as  is  also  the  temperature  at  which  the  transformation 
is  complete. 

For  pure  substances  there  is,  therefore,  a  perfectly  definite  re- 
lation between  the  pressure  and  the  temperature  at  which  liquid 
and  vapour  can  exist  in  equilibrium,  and  the  two  increase  and  de- 
crease together.  This  pressure  is  called  the  vapour  pressure  of  the 
substance  at  the  corresponding  temperature,  and  the  temperature 
is  called  the  boiling  point  of  the  substance  at  the  corresponding 
pressure.  When  we  speak  of  the  boiling  point  simply  we  always 
mean  the  boiling  point  corresponding  to  a  pressure  of  one  atmos- 
phere, —  the  temperature  at  which  boiling  would  begin  in  an  open 
vessel. 

53.  THE  VAPOUR  PRESSURE  OF  WATER.  —  The  relation  between 
temperature  and  vapour  pressure  for  water  is  shown  in  the  accom- 

5 


66 


FUNDAMENTAL   PRINCIPLES   OF  CHEMISTRY 


panying  table.  Temperatures  are  given  in  Centigrade  degrees 
and  pressures  in  centimetres  of  mercury.  Two  sets  of  values  are 
given  below  0°.  The  first  of  these  corresponds  to  solid  water  (ice) ; 
the  second,  to  super-cooled  liquid  water. 


VAPOR  PRESSURE  OF  WATER. 


Tempera- 
ture. 

Pressure. 

Tempera- 
ture. 

Pressure. 

Ice. 

Liquid  Water. 

Liquid  Water. 

-  15° 

0.126  cm. 

0.145  cm. 

+     18° 

1.538  cm. 

-  14° 

0.138  cm. 

0.157  cm. 

+     19° 

1.637  cm. 

-  13° 

0.151  cm. 

0.171  cm. 

+     20° 

1.741  cm. 

-  12° 

0.165  cm. 

0.185  cm. 

+     21° 

1.850  cm. 

-  11° 

0.181  cm. 

0.200  cm. 

+     22° 

1.966  cm. 

-  10° 

0.197  cm. 

0.216  cm. 

+     23° 

2.088  cm. 

-     9° 

0.215  cm. 

0.234  cm. 

+     24° 

2.218  cm. 

-     8° 

0.235  cm. 

0.252  cm. 

+     25° 

2.355  cm. 

-     7° 

0.256  cm. 

0.272  cm. 

+     30° 

3.156  cm. 

-    6° 

0.279  cm. 

0.294  cm. 

+     35° 

4.185  cm.. 

-     5° 

0.303  cm. 

0.317  cm. 

+     40° 

5.497  cm. 

-     4° 

0.330  cm. 

0.341  cm. 

+     45° 

7.150  cm. 

-    3° 

0.359  cm. 

0.368  cm. 

+     50° 

9.217  cm. 

-     2° 

0.389  cm. 

0.396  cm. 

+     55° 

11.78    cm. 

-     1° 

0.422  cm. 

0.426  cm. 

+     60° 

14.92    cm. 

-    0° 

0.458  cm. 

0.458  cm. 

+     65° 

18.75    cm. 

+     1° 

0.492  cm. 

+     70° 

23.38    cm. 

+     2° 

0.529  cm. 

+     75° 

28.93    cm. 

+    3° 

0.568  cm. 

+    80° 

35.55    cm. 

+     4° 

0.609  cm. 

+    85° 

43.38    cm. 

+     5° 

0.653  cm. 

+    90° 

52.60    cm. 

+     6° 

0.700  cm. 

+    95° 

63.40    cm. 

+     7° 

0.749  cm. 

+  100° 

76.00    cm. 

+    8° 

0.802  cm. 

+  110° 

107.5      cm. 

+    9° 

0.858  cm. 

+  120° 

149.1      cm. 

+  10° 

0.917  cm. 

+  130° 

203.0      cm. 

+  11° 

0.981  cm. 

+  140° 

272         cm. 

+  12° 

1.048  cm. 

+  150° 

358         cm. 

+  13° 

1.119  cm. 

+  160° 

465         cm. 

-f  14° 

1.194  cm. 

+  170° 

596         cm. 

+  15° 

1.273  cm. 

+  180° 

755         cm. 

+  16° 

1.357  cm. 

+  190° 

944         cm. 

+  17° 

1.445  cm. 

+  200° 

1169         cm. 

CHANGE   OF   STATE   AND   EQUILIBRIUM 


67 


54.  DIAGRAM.  —  This  relation  can  also  be  made  clear  by  laying 
off  temperatures  along  a  horizontal  straight  line  in  a  plane,  and 
then  laying  off  the  pressure  (in  centimetres  of  mercury,  for  ex- 
ample), corresponding  to  each  temperature,  along  a  vertical  line. 
Arbitrary  units  of  lengths  are  to  be  chosen  for  each  quantity  with 
regard  to  the  scale  in  which  the  drawing  is  to  be  carried  out.  The 
upper  ends  of  the  pressure  values  will  then  all  lie  on  a  continuous 
curved  line  which  is  called  the  vapour  pressure  curve,  or  the  curve 


80 
-^70 


5O° 
TEMPERA  TURE 

FIG.  1. 


of  saturated  vapour.  The  vapour  pressure  curves  of  all  substances 
are  similar  in  shape,  and  they  are  like  the  vapour  pressure  curve 
of  water  shown  in  Fig.  1.  They  all  turn  their  concave  side  up- 
ward and  become  steeper  with  increasing  temperature.  The 
course  and  position  of  the  curve  is,  however,  very  different  for 
different  substances,  and  there  are  no  two  substances  which  are 
different  in  other  things  but  which  have  the  same  vapour  pressure 


68  FUNDAMENTAL  PRINCIPLES  OF  CHEMISTRY 

curves.    These  curves  are  just  as  much  specific  properties  of  sub- 
stances as  are  their  densities  or  specific  volumes. 

It  happens,  however,  that  two  different  substances  do  have  the 
same  vapour  pressure  at  the  same  temperature.  Their  vapour 
pressures  will,  however,  be  different  at  all  other  temperatures, 
and  the  two  vapour  pressure  lines  have  crossed  each  other  at  the 
temperature  in  question.  But  this  is  a  rare  case. 

In  general  it  is  not  necessary  to  determine  the  whole  course  of 
the  vapour  pressure  curves  of  substances  in  order  to  determine 
whether  or  not  they  are  different.  It  is  usually  sufficient  to  deter- 
mine one  single  point.  This  point  is  usually  the  boiling  point  at 
atmospheric  pressure,  because  this  is  the  easiest  point  to  deter- 
mine, and  the  boiling  points  of  various  substances  are  frequently 
used  as  an  indication  of  difference  or  similarity. 

55.  CHANGE  OF  VOLUME  DURING  EVAPORATION.  —  When 
temperature  and  pressure  are  so  regulated  that  liquid  and  vapour 
can  exist  together,  the  following  changes  take  place  in  the  volume 
occupied  by  the  two  phases. 

The  liquid  expands  as  the  temperature  rises.  Of  course  the 
increase  of  volume  is  less  when  the  pressure  is  increased  at  the 
same  time  than  it  would  be  if  the  pressure  were  kept  constant, 
but  the  influence  of  pressure  is  so  small  that  the  resultant  appears 
as  an  increase  of  volume.  This  increase  is  a  very  small  one,  be- 
cause of  the  slight  coefficient  of  expansion  of  liquids. 

With  the  vapour  it  is  entirely  different.  As  described  by  Boyle's 
Law,  the  volume  is  inversely  proportional  to  the  pressure.  At  the 
low  vapour  pressures  which  correspond  to  low  temperatures  it  is 
very  great,  but  it  becomes  very  rapidly  smaller  as  the  tempera- 
ture rises,  corresponding  to  a  rapid  increase  in  the  vapour  pres- 
sure. In  this  case  also  an  opposing  effect  is  present,  for,  as  the 
result  of  an  increase  in  temperature,  the  specific  volume  would  in- 
crease, according  to  the  Law  of  Gay-Lussac,  provided  the  pressure 
remains  the  same.  But  the  influence  of  change  of  pressure  is  so 
great  that  the  vapour  which  is  in  equilibrium  with  the  liquid 


CHANGE   OF   STATE   AND   EQUILIBRIUM  69 

behaves  in  the  opposite  way  from  the  liquid  itself.  Its  specific 
volume  decreases  with  rising  temperature,  and  decreases  very 
rapidly. 

When  the  specific  volume  of  the  vapour  in  question  has  once 

been  measured,  the  constant  r  in  the  gas  equation  ±=-  =r  can  be 

determined  for  this  vapour  by  inserting  the  observed  values  for 
volume,  temperature,  and  pressure  in  the  formula.  If  r  is  known 
this  process  can  be  reversed  and  the  volume  calculated  for  each 
value  of  pressure  and  temperature  according  to  the  formula 

rT 
v=  — .     It  is  easy  to  calculate  the  specific  volume  of  a  saturated 

P 

vapour  in  this  way  if  the  vapour  pressure  curve  is  known,  for  this 

curve  represents  corresponding  values  of  pressure  and  tempera- 
ture for  equilibrium  between  the  vapour  and  liquid. 

The  gas  equation  only  gives  correct  results  when  the  specific 
volume  is  large.  As  it  becomes  small,  because  of  the  rapidly  in- 
creasing pressure  corresponding  to  increasing  temperature,  calcu- 
lations made  by  means  of  the  simple  gas  formula  become  less  and 
less  accurate.  The  deviations  are  of  such  a  nature  that  the  real 
volume  always  comes  out  smaller  than  the  calculated  one,  and 
this  deviation  becomes  greater  as  the  pressure  is  increased. 

Additions  have  been  made  to  the  gas  equation  to  express  these 
deviations,  but  we  cannot  take  them  up  here.  The  following 
table  gives  the  same  relations  for  liquid  water  and  water  vapour 
again,  the  results  having  been  obtained  directly  from  experimental 
measurements.  The  first  column  contains  the  temperature  in 
Centigrade  degrees;  the  second,  the  vapour  pressures  of  water 
at  these  temperatures,  expressed  in  centimetres  of  mercury;  the 
third  and  fourth  give  the  values  for  the  specific  volume  of  the 
saturated  vapour  and  that  of  liquid  water,  expressed  in  cubic 
centimetres.  It  is  evident  that  the  specific  volume  of  the  vapour 
decreases  very  rapidly  with  rising  temperature,  while  that  of 
liquid  water  increases  slowly,  as  indicated  above. 


70 


FUNDAMENTAL   PRINCIPLES   OF  CHEMISTRY 


•'  Tempera- 

Vapor 

Specific  Volume. 

ture. 

Pressure. 

Vapor. 

Liquid. 

0° 

0.46 

203500 

1.00 

20° 

1.74 

57800 

1.002 

50° 

9.20   ' 

12030 

1.012 

100° 

76.0 

1681 

1.043 

120° 

149.1 

945 

1.060 

160° 

465 

317 

1.101 

180° 

765 

203 

1.127 

200° 

1169 

140 

1.158 

It  will  be  seen  from  these  values  that  a  great  increase  in  volume 
results  from  the  change  from  liquid  water  into  water  vapour.  At 
0°  C.  the  volume  increase  is  about  200,000  times.  At  200°  the 
increase  is  only  about  120  times. 

56.  HEAT  OF  VAPORIZATION.  —  When  a  liquid  changes  into  a 
gas  the  change  is  accompanied  by  a  change  of  volume.  At  the 
same  time  a  very  considerable  amount  of  heat  must  be  absorbed 
if  the  temperature  is  to  remain  constant,  or,  as  we  say,  if  the  process 
is  to  take  place  isothermally.  This  heat  has  been  called  latent  heat, 
because  it  is  added  to  the  system  without  producing  a  rise  of 
temperature.  This  expression  is,  however,  only  a  makeshift,  which 
was  applied  because  the  phenomenon  was  not  understood,  that 
is,  its  connection  with  other  facts  was  not  known.  The  more 
general  explanation  is,  that  every  chemical  process  in  which  a 
given  body  is  transformed  into  another  having  other  properties 
is  accompanied  by  a  change  in  the  energy  of  that  body.  This 
energy  may  appear  in  many  different  ways.  A  change  of  volume 
under  a  certain  pressure  represents  an  amount  of  work  which  is 
measured  by  the  product  of  pressure  and  volume.  Energy,  in 
general,  means  either  work  or  anything  which  can  be  obtained 
from  work  or  transformed  into  work.  Since  work  can  always  be 
transformed  into  a  proportional  amount  of  heat,  the  latter  is  also 


CHANGE   OF  STATE   AND   EQUILIBRIUM  71 

a  form  of  energy,  and  confirmation  of  this  is  found  in  the  fact  that 
heat  can  be  transformed  into  mechanical  work  by  means  of  steam 
or  gas  engines.  The  above  principles  can  therefore  be  expressed 
by  saying  that  one  body  can  never  be  transformed  into  another 
without  the  co-operation  of  work.  This  work  can  be  either  posi- 
tive or  negative,  that  is  to  say,  energy  can  either  be  taken  in  or 
given  out  during  the  process.  During  the  evaporation  of  a  liquid 
heat  is  taken  in;  during  the  liquefaction  of  a  vapour  an  equal 
amount  of  heat  is  given  out.  If  we  investigate  evaporation  at 
various  temperatures  and  pressures  it  is  found  that  at  high  values 
of  these  factors  the  heat  of  vaporization  becomes  smaller  and 
smaller  as  the  values  of  temperature  and  pressure  increase. 

57.  THE  MEASUREMENT  OF  QUANTITY  OF  HEAT.  —  Since 
heat  is  a  form  of  energy  it  is  a  quantity  in  the  narrower  sense  of 
the  word,  which  can  be  added,  and  which  is  therefore  capable  of 
direct  measurement  when  once  the  unit  has  been  determined. 
It  would  be  better  to  use  the  same  unit  for  all  the  forms  of  energy, 
for  then  amounts  of  energy  which  are  produced  from  each  other, 
or  which  could  be  transformed  into  each  other,  would  be  char- 
acterized by  the  same  number.  There  is  such  a  system  of  units, 
and  it  is  called  the  absolute  system,  but  it  has  not  yet  been  gen- 
erally introduced.  Especially  in  the  case  of  heat  another  unit 
is  in  general  use,  which  was  determined  upon  at  a  time  when  we 
knew  nothing  about  the  mutual  transformation  of  the  various 
forms  of  energy.  This  unit  is  based  upon  the  properties  of  the 
most  familiar  of  all  pure  substances,  water,  as  weight  and  density 
are  also  based  on  water.  The  unit  chosen  for  quantity  of  heat 
was  the  amount  which  would  raise  the  temperature  of  a  gramme 
of  water  1°  C.  This  unit  is  slightly  variable  with  temperature, 
and  an  agreement  was  made  to  base  this  definition  on  18°,  which 
was  taken  as  being  ordinary  room  temperature.  This  unit  is 
called  a  calorie,  which  is  abbreviated  to  cal. 

If  a  gramme  of  water  vapour  at  atmospheric  pressure  is  passed 
into  a  weighed  amount  of  water,  the  water  becomes  warmer,  and 


72  FUNDAMENTAL   PRINCIPLES  OF  CHEMISTRY 

its  rise  of  temperature  is  very  much  greater  than  would  result 
from  adding  one  gramme  of  liquid  water  at  the  same  temperature 
as  the  steam,  that  is,  at  100°  C.  The  difference,  which  corresponds 
to  the  heat  of  liquefaction  of  one  gramme  of  water  vapour  under 
the  given  conditions,  is  536  cal.  This  number  is  found  by  mul- 
tiplying the  weight  in  grammes  of  the  water  used  by  the  rise  of 
temperature  in  degrees  Centigrade.  The  quantity  of  heat  is  pro- 
portional to  the  quantity  of  water  heated,  and  also  to  the  rise  of 
temperature;  it  is  therefore  proportional  to  the  product  of  these 
two  quantities.  • 

That  division  of  chemistry  which  has  to  do  with  changes  of 
heat  accompanying  transformations  between  substances  is  called 
thermo-chemistry.  Just  as  we  can  determine  the  heat  value  cor- 
responding to  the  transformation  of  water  vapour  into  liquid 
water,  and  vice  versa,  so  we  can  find  the  corresponding  heat  value 
for  any  other  chemical  process  by  carrying  out  the  necessary 
measurements. 

58.  ENTROPY.  —  Two  forms  of  energy,  volume  energy  and  heat, 
are  involved  in  the  phenomena  of  evaporation,  and  they  exhibit 
a  great  similarity.  Volume  energy  can  be  considered  as  the  product 
of  two  factors,  the  pressure  and  the  increase  of  volume ;  and  in  the 
same  way  a  change  in  heat  energy  can  be  considered  as  the  product 
of  two  factors,  of  which  one  is  the  temperature.  This  corresponds 
to  the  pressure,  for  both  values  are  intensities  and  not  quantities. 
That  this  is  true  of  temperature  is  evident  from  the  fact  that  two 
bodies  which  have  the  same  temperature  do  not  show  twice  the 
temperature  when  they  are  brought  together.  The  temperature 
remains  unchanged.  The  other  factor,  which  is  a  quantity  in  the 
narrower  sense,  and  which  is  therefore  additive,  is  not  as  well 
known  as  volume,  which  is  the  corresponding  factor  of  volume 
energy. 

This  comes  from  the  fact  that  we  have  become  accustomed  in 
working  with  heat  to  use  the  energy  itself,  that  is,  the  amount  of 
heat,  and  with  this,  one  of  its  factors,  temperature.  The  other 


CHANGE  OF  STATE  AND   EQUILIBRIUM  73 

factor  has  so  far  been  used  only  in  mathematical  physics,  although 
it  offers  no  greater  difficulties  to  the  understanding  than  a  quan- 
tity of  electricity  or  a  momentum.  In  the  case  of  volume  energy 
the  matter  is  reversed.  Here  the  two  factors,  pressure  and  volume, 
are  in  common  use,  while  volume  energy  itself  is  by  no  means  so 
generally  used. 

The  capacity  factor  of  heat  energy  is  called  entropy;  the  product 
of  entropy  and  temperature  gives  heat  energy.  We  must  there- 
fore be  able  to  find  entropy  by  dividing  energy  by  temperature; 
536  heat  units  are  absorbed  by  a  gramme  of  water  changing  to 
vapour  under  atmospheric  pressure.  The  corresponding  increase 
of  entropy  is  to  be  found  by  dividing  this  number  by  the  tempera- 
ture 100°  C.  or  373  A.,  and  the  result  is  |f|  =  1.44  entropy  units. 

59.  THE  CRITICAL  POINT.  —  The  facts  we  have  just  been  con- 
sidering give  rise  to  several  general  questions.  First,  vapour 
pressure  increases  with  rising  temperature.  Can  this  go  on  with- 
out limit?  Second,  the  specific  volumes  of  liquid  and  vapour 
approach  each  other  with  rising  temperature,  and  the  change  of 
volume  during  vaporization  becomes  smaller  and  smaller.  Will 
it  finally  become  zero?  Third,  the  heat  of  vaporization  (or  the 
change  of  entropy)  becomes  smaller  and  smaller  with  rising  tem- 
perature. Will  it  also  finally  become  zero  ?  Fourth,  when  both 
these  things  become  zero,  in  case  this  happens,  will  they  arrive 
at  zero  simultaneously  or  at  different  points? 

These  questions  have  been  answered  as  follows  by  experiments. 
As  the  temperature  is  increased,  the  vapour  pressure,  that  is,  the 
pressure  of  the  vapour  which  is  in  equilibrium  with  the  liquid, 
does  not  increase  continuously.  The  vapour  pressure  line  has  a 
definite  end  at  a  highest  temperature  and  a  highest  pressure,  and 
these  two  highest  values  correspond  to  the  point  where  the  specific 
volume  of  the  vapour  is  the  same  as  that  of  the  liquid.  At  the  same 
point  the  heat  of  vaporization  and  the  change  of 'entropy  both  be- 
come zero,  and  there  remains  no  difference  whatever  between  the 
liquid  and  its  vapour.  This  means,  of  course,  that  liquid  and 


74 


FUNDAMENTAL   PRINCIPLES   OF  CHEMISTRY 


vapour  cease  to  exist  in  contact  with  each  other,  and  this  means 
the  end  of  the  vapour  pressure  line.  Above  this  point  there  is  no 
longer  a  transformation  of  liquid  into  vapour,  and  any  values 
whatever  may  be  given  to  pressure  and  temperature.  All  this  is 

expressed  in  the  diagram  of 
Fig.  2.  Here  densities  (not  spe- 
cific volumes)  of  vapour  and 
liquid  have  been  plotted  horizon- 
tally, and  temperature  vertically. 
The  density  of  the  vapour  in- 
creases with  rising  temperature 
while  that  of  the  liquid  decreases. 
The  two  approach  one  another 
and  finally  coincide  at  a  definite 
point. 

This  point  is  called  the  critical 
point,  and  it  corresponds  to  a 
definite  temperature  and  a  defi- 
nite pressure  which  are  called 


DENSITY  the  critical  temperature  and  the 

FIG>  2.  critical  pressure.     The   common 

specific  volume  at  this  point  is 

called  the  critical  volume.  It  is  evident  that  the  critical  point  cor- 
responds to  a  point  where  liquid  and  vapour  become  identical. 

The  critical  data  vary  with  the  nature  of  the  substance,  and  we 
find  critical  temperatures  lying  at  every  part  of  our  temperature 
scale.  Critical  pressures  lie  closer  together  and  have  values  be- 
tween 25  and  100  atmospheres,  depending  on  the  nature  of  the 
substance.  Critical  volumes  vary  from  1.5  to  5,  and  therefore 
show  no  very  great  difference.  The  critical  volume  is,  in  general, 
greater  if  the  critical  temperature  is  high. 

It  is  easy  to  observe  the  most  important  phenomenon  corre- 
sponding to  the  critical  point,  that  is,  the  identity  of  liquid  and 
vapour,  by  sealing  up  a  rather  volatile  liquid  in  an  exhausted  glass 


CHANGE   OF  STATE   AND   EQUILIBRIUM  75 

tube  so  that  it  fills  about  one  half  the  volume  of  the  tube.  If  the 
temperature  is  now  increased,  the  difference  between  the  liquid 
and  the  vapour  above  it  becomes  smaller  and  smaller,  and  at  the 
critical  temperature  the  surface  between  them  disappears  and 
the  tube  is  filled  with  a  homogeneous  substance.  If  the  tube  is 
then  slowly  cooled  a  peculiar  brownish  fog  appears  suddenly  at 
the  critical  temperature.  The  denser  liquid  appears  immediately 
in  the  lower  part  of  the  tube,  the  lighter  vapour  collects  above  it  in 
the  upper  part. 

60.  PHASES.  —  The  changes  of  state  just  described,  which  are 
produced  in  a  substance  by  changes  in  temperature  and  pressure, 
may  be  considered  processes  in  which  mixtures  result  from  homo- 
geneous substances.  A  mixture  of  gas  and  liquid  is  produced 
from  a  homogeneous  gas  by  compression  and  cooling.  If  a  homo- 
geneous liquid  is  cooled,  there  results  a  mixture  of  it  and  a  solid 
substance.  If  the  temperature  is  still  further  lowered,  the  mixture 
changes  into  a  homogeneous  substance  again,*  the  constituent 
corresponding  to  the  first  state  disappearing  and  leaving  its  suc- 
cessor, which  corresponds  to  another  state. 

The  components  of  mixtures  produced  by  a  transformation  of 
this  sort  are  called  phases.  Phases,  therefore,  are  homogeneous 
substances  which  appear  in  mixtures.  They  may  be  either  pure 
substances  or  solutions.  In  our  general  definition  of  a  substance 
we  took  no  account  of  shape  or  quantity.  Our  definition  of  a  phase 
is  the  same  in  this  respect,  and  all  the  parts  of  a  mixture  which 
have  corresponding  specific  properties  are  included  in  one  phase. 

Two  or  more  phases  are  in  equilibrium  when  they  can  exist  to- 
gether without  any  effect  on  each  other's  properties. 

The  first  condition  to  be  realized  here  is  that  they  must  all  be 
under  the  same  pressure  and  at  the  same  temperature,  otherwise 
it  is  impossible  that  they  should  exist  together  without  any  change 

*  Mixtures  may  result  from  solutions  under  these  circumstances.  A  salt 
solution,  for  example,  may  form  a  mixture  of  solid  water  and  solid  salt.  The 
facts  as  given  in  the  text  hold  for  pure  substances  and  the  case  of  solutions 
will  be  taken  up  later  in  a  special  chapter. 


76  FUNDAMENTAL   PRINCIPLES  OF  CHEMISTRY 

taking  place.  Beside  this,  other  conditions  must  be  fulfilled,  and 
we  will  consider  these  a  little  later.  If  two  or  more  homogeneous 
substances  are  brought  together  they  do  not,  in  general,  form 
phases  which  are  in  equilibrium.  They  usually  affect  each  other 
mutually  even  when  pressure  and  temperature  are  the  same.  The 
processes  which  take  place  under  these  circumstances  make  up  the 
greater  part  of  what  is  called  chemistry. 

61.  DEGREES  OF  FREEDOM.  —  If  pressure  and  temperature  are 
considered  as  variable  we  can  affect  the  condition  of  substances  in 
two  ways,  and  it  is  only  when  definite  values  have  been  given  to 
these  two  factors  that  the  condition  of  a  substance  is  determined. 
We  are  free  to  do  as  we  choose  with  temperature  and  pressure  (to 
a  certain  extent  at  least,  which  is  bounded  by  the  appearance  of 
new  states),  and  it  is  therefore  said  that  each  substance  possesses 
two  degrees  of  freedom.  It  makes  no  difference  whether  the  sub- 
stance in  question  is  a  pure  substance  or  a  solution,  whether  it  is 
solid,  liquid,  or  gaseous,  although  the  effect  of  pressure  and  tem- 
perature on  a  solid  is  very  small  and  on  a  gas  is  very  great. 

Conditions  are  changed,  as  we  have  seen,  when  a  second  phase 
appears.  If  we  have  made  the  condition  that  liquid  and  vapour 
shall  exist  together,  we  have  used  up  one  of  our  "  freedoms,"  and 
only  one  is  left.  This  corresponds  to  the  fact  that  to  each  tempera- 
ture there  corresponds  a  perfectly  definite  vapour  pressure  which  is 
only  dependent  upon  the  nature  of  the  liquid.  If  we  have  decided 
upon  the  temperature  in  this  case  we  are  no  longer  free  in  the 
choice  of  a  pressure.  And  in  the  same  way  we  no  longer  have  any 
choice  of  a  temperature  when  we  have  prescribed  a  certain  pres- 
sure. Temperature  can  then  have  only  one  value,  and  that  is  the 
boiling  point  of  the  liquid  at  the  pressure  chosen.  If  we  change 
the  temperature  or  the  pressure  under  these  conditions,  one  of  the 
phases  will  disappear. 

We  may  conclude  from  this  that  the  condition  that  a  second 
phase  shall  exist  in  contact  with  a  given  phase  is  the  same  thing 
as  disposing  of  one  degree  of  freedom,  and  that  therefore  the  sum 


CHANGE  OP  STATE  AND  EQUILIBRIUM  77 

of  phases  and  degrees  of  freedom  is  a  definite  number.  How  large 
this  number  is  depends  upon  whether  we  are  dealing  with  a  pure 
substance  or  a  solution.  The  simpler  considerations  apply  to  the 
pure  substances,  and  we  will  therefore  take  up  their  behaviour 
first. 

If  a  new  phase  is  produced  from  a  pure  substance  by  a  proper 
variation  of  pressure  and  temperature,  the  properties  of  both 
phases  are  determined,  for  although  we  can  change  the  relative 
proportions  in  which  the  two  phases  exist  by  changing  the  volume 
or  the  entropy,  we  cannot  produce  any  change  whatever  in  the 
properties  of  either  phase.  This  is,  of  course,  the  definition  of  a 
pure  substance.  It  exhibits  no  change  of  properties  when  it  is 
partially  transformed  into  a  new  phase.  We  have,  therefore,  no 
further  freedom  to  produce  change. 

The  number  of  degrees  of  freedom  belonging  to  a  single  phase  is 
two,  for  we  can  give  it  any  temperature  and  any  pressure  within 
the  limits  between  which  the  substance  remains  in  the  same  state. 
If  we  now  fix  the  condition  that  a  second  phase  is  to  exist  in  equi- 
librium with  the  first,  we  have  disposed  of  one  degree  of  freedom, 
and  only  one  remains.  This  is  another  expression  for  the  fact 
already  described,  that  when  two  phases  of  a  pure  substance  are 
in  equilibrium  only  one  definite  temperature  corresponding  to  each 
pressure  (and  one  pressure  corresponding  to  each  temperature)  can 
be  found  at  which  the  two  phases  will  continue  to  exist  together. 
If  a  third  phase  be  added,  the  last  degree  of  freedom  has  been  dis- 
posed of,  and  we  will  see  that  in  a  pure  substance  three  phases 
can  only  exist  together  at  one  definite  pressure  and  at  one 
definite  temperature. 

If  we  sum  up  phases  and  degrees  of  freedom  in  each  case  the 
result  is  always  three.  One  phase  has  two  degrees  of  freedom; 
two  phases,  one ;  three  phases,  none.  For  pure  substances  we  may 
state  the  law :  The  sum  of  phases  and  degrees  of  freedom  is  three. 
This  is  called  the  phase  rule. 

This  rule  does  not  apply  to  solutions.    In  the  case  of  a  solution 


78  FUNDAMENTAL   PRINCIPLES   OF  CHEMISTRY 

two  phases  can  exist  in  equilibrium  at  a  given  pressure,  not  only  at 
one  temperature,  but  at  any  number  of  different  temperatures. 
One  of  the  characteristics  of  a  solution  is  the  fact  that  its  boiling 
point  does  not  remain  constant  at  constant  pressure,  while  more 
and  more  of  the  second  phase  is  being  produced,  but  rises  continu- 
ally as  the  transformation  proceeds.  The  same  statement  applies 
to  the  pressure  when  the  temperature  is  kept  constant.  The  num- 
ber of  degrees  of  freedom  is  therefore  greater  in  a  solution  than  in 
a  pure  substance.  How  large  the  number  is  depends  upon  the  na- 
ture of  the  solution,  and  this  we  shall  consider  later.  Be  it  said, 
however,  that  solutions  are  classified  by  the  number  of  degrees  of 
freedom  which  they  possess  when  another  phase  is  present.  As 
long  as  no  second  phase  is  in  contact  with  a  solution  it  acts  just 
like  a  pure  substance  and  possesses  only  two  degrees  of  freedom 
in  temperature  and  pressure. 

62.  SUBLIMATION.  —  In  a  few  cases  the  substance  produced  from 
a  gas  by  lowering  the  temperature  is  not  a  liquid  but  a  solid,  and 
in  this  case  the  solid  changes  on  being  heated  into  a  gas  or  vapour. 
Laws  which  describe  these  transformations  have  exactly  the  same 
form  as  those  corresponding  to  the  transformation  of  gas  into 
liquid,  and  vice  versa.  For  pure  substances  each  new  temperature 
corresponds  to  a  definite  pressure  at  which  vapor  and  solid  can 
exist  together.  The  word  "  sublimation  "  is  commonly  applied  to 
the  transformation  of  a  vapour  into  a  solid  body. 

If  the  vapour  pressure  curve  of  a  solid  body  is  followed  upward 
into  higher  and  higher  pressures  and  temperatures,  the  critical 
point  is  not  reached  directly.  In  all  the  cases  which  have  so  far 
been  investigated  a  transformation  of  the  solid  body  into  a  liquid 
takes  place  before  the  critical  point  is  reached.  The  solid  melts. 
The  liquid  thus  produced  then  has  its  own  vapour  pressure  line, 
which  ends  at  the  critical  point. 

Special  relations  appear  in  the  case  of  solutions,  for  while  all 
gases  are  soluble  in  one  another  without  limit,  a  mutual  solubility 
is  a  comparatively  rare  phenomenon  among  solids.  When,  there- 


CHANGE   OF  STATE  AND   EQUILIBRIUM  79 

fore,  various  solid  bodies  separate  from  a  gaseous  solution  as  a 
result  of  decrease  of  temperature  or  increase  of  pressure,  these 
do  not,  as  a  rule,  form  solutions,  but  mixtures  of  several  solids. 

63.  SUSPENDED  TRANSFORMATION. — It  has  been  tacitly  assumed 
in  the  foregoing  that  when  the  conditions  of  temperature  and  pres- 
sure are  fulfilled  under  which  a  new  phase  can  exist,  this  new 
phase  will  appear.  This  assumption  is  not  quite  correct,  for  there 
are  many  cases  where  the  new  phase  does  not  immediately  appear. 
It  is,  however,  true  that  when  under  such  circumstances  a  little  of 
the  new  phase  is  present,  its  formation  continues  just  as  would  be 
expected  from  existing  conditions.  It  is  evident  from  this  that  the 
absence  of  a  trace  of  a  new  phase  is  necessary  if  its  formation  is 
not  to  take  place  under  conditions  which  lead  us  to  expect  it. 

If  special  precautions  are  taken  it  is  quite  possible  to  heat  water 
to  a  temperature  above  100°  C.  without  its  beginning  to  boil,  and 
without  any  rapid  change  into  vapour.  If  water  drops  are  formed 
in  hot  fat  or  oil  the  temperature  can  be  raised  many  degrees  above 
100°  C.  without  the  appearance  of  the  gaseous  phase.  If  the 
temperature  is  further  increased  vaporization  usually  begins  sud- 
denly, and  because  the  temperature  is  high  a  very  large  amount  of 
vapour  is  suddenly  produced  with  a  resulting  explosion. 

In  the  same  way  water  vapour  can  exist  at  pressures  which  are 
greater  than  the  vapour  pressure  at  which  it  is  in  equilibrium  with 
liquid  water.  It  is  not  easy  to  arrange  a  laboratory  experiment  to 
show  this,  but  the  process  is  a  common  one  in  nature,  and  appears 
when  masses  of  air  containing  water  vapour  are  cooled  because  of 
a  meteorological  change.  When  water  vapour  in  this  condition 
comes  in  contact  with  liquid  water  in  the  form  of  rain  or  fog  a 
sudden  change  takes  place  which  results  in  cloud-bursts  and 
rain-storms. 

These  facts  are  all  in  agreement  with  the  phase  rule  and  present 
examples  of  its  application.  As  long  as  liquid  water  only  is  present 
without  vapour  we  have  to  do  with  only  one  phase,,  and  pressure 
and  temperature  are  free.  A  trace  of  the  other  phase  requires  a 


80  FUNDAMENTAL  PRINCIPLES  OF  CHEMISTRY 

new  set  of  conditions.    The  two  phases  are  then  existent  simultane- 
ously and  one  degree  of  freedom  disappears. 

A  condition  of  the  kind  just  described,  in  which  a  new  phase 
could  exist  but  as  a  matter  of  fact  does  not  appear,  can  be  brought 
about  by  overstepping  the  conditions  of  saturation  or  equilibrium. 
Such  a  condition  is  said  to  be  one  of  supersaturation.  The  condi- 
tion can  persist,  but  a  sudden  transformation  takes  place  as  soon 
as  a  little  of  the  possible  new  phase  is  added.  It  is  therefore  not 
stable  in  the  strict  sense,  and  it  is  called  the  metastable  condition. 
If  the  supersaturation  is  carried  further,  almost  any  circumstance 
may  cause  the  appearance  of  the  new  phase,  and  there  is  a  limit 
at  which  the  new  phase  appears  of  its  own  accord,  that  is  to  say, 
without  the  addition  of  a  small  amount  of  it.  Beyond  this  point 
lies  what  is  called  the  labile  condition.  Throughout  all  these  vari- 
ous conditions  the  vapour  retains  its  specific  properties,  changing 
continuously  with  temperature  and  pressure.  All  these  conditions 
are  only  characterized  by  the  appearance  or  non-appearance  of  a 
new  phase,  and  they  are  therefore  not  conditions  of  the  vapour  as 
such,  but  only  conditions  belonging  to  the  vapour  in  connection 
with  the  new  phase.  The  saturation  point  of  a  vapour  is  therefore 
in  no  way  indicated  by  any  characteristic  change  in  its  specific 
properties.  This  should  be  kept  clearly  in  mind  in  the  general 
consideration  of  the  facts,  as  many  errors  have  been  caused  by 
lack  of  care  in  its  discussion. 


(6)  The  Equilibrium  Solid-Liquid 

64.  MELTING  AND  SOLIDIFICATION.  —  It  is  evident  from  the 
foregoing  how  liquids  will  behave  when  the  temperature  is  raised  or 
the  pressure  is  lowered.  They  change  into  gases.  We  must  now 
investigate  what  happens  to  liquids  when  the  temperature  is 
lowered  and  the  pressure  raised.  Let  us  examine  the  first  case. 

When  a  liquid  is  cooled  to  a  sufficiently  low  temperature  it 
changes  into  a  solid;  it  solidifies.  With  the  aid  of  the  very  low 


UNIVERSITY 


CHANGE  OF  STATE  AND  EQUILIBRIUM  81 

temperatures  which  have  been  attained  in  the  last  few  years  this 
statement  has  been  proven  to  be  a  very  general  one. 

This  transformation  from  one  state  to  another  is  completely  an- 
alogous to  the  change  from  a  gas  into  a  liquid.  Here  again  two 
cases  are  to  be  distinguished:  either  the  entire  transformation 
takes  place  completely  at  one  definite  temperature,  —  the  freezing 
point,  or  the  temperature  sinks  lower  and  lower  during  the  trans- 
formation, so  that  solidification  takes  place  within  a  temperature 
region  of  finite,  but  often  very  great,  extent.  In  the  first  case 
we  have  to  do  with  a  pure  substance;  in  the  second,  with  a 
solution. 

The  question  immediately  arises  whether  a  substance  which  has 
been  shown  to  be  a  solution  by  the  vaporization  test  (by  its  vari- 
able boiling  point)  will  also  act  like  a  solution  during  solidifica- 
tion, exhibiting  here  a  variable  freezing  point.  The  answer  is  in 
the  affirmative.  A  substance  which  is  characterized  as  a  solution 
in  the  one  case  will  also  act  like  a  solution  in  the  other  case.  The 
character  of  a  pure  substance  or  a  solution  can  therefore  be  deter- 
mined by  either  method. 

The  inverse  of  the  process  of  solidification  is  melting,  which  is 
the  change  from  the  solid  into  the  liquid  condition.  Exactly  similar 
laws  are  observable  here.  Either  the  whole  process  of  melting 
takes  place  at  a  constant  temperature,  that  of  the  melting  point, 
indicating  that  we  are  dealing  with  a  pure  substance,  or  it  takes 
place  at  a  rising  temperature,  variable  within  a  finite  range.  In 
the  latter  case  we  have  to  do  with  a  solution. 

The  fact  that  pure  substances  (pure  water,  for  example)  melt 
and  freeze  at  a  constant  temperature  was  observed  a  long  time 
ago.  This  fact  determines  the  use  of  the  melting  point  of  water 
as  the  lower  fundamental  point  in  the  making  of  thermometers 
and  in  the  definition  of  temperature.  Conversely,  the  melting 
point  can  be  used  as  well  as  the  boiling  point  to  characterize  a  pure 
substance,  or  to  prove  whether  a  substance  under  investigation 
is  a  pure  substance  or  a  solution.  Melting  point  and  freezing 
6 


82  FUNDAMENTAL   PRINCIPLES   OF   CHEMISTRY 

point  are  the  same  for  pure  substances.  It  is  simply  the  tempera- 
ture at  which  the  liquid  and  solid  phases  are  in  equilibrium. 

65.  THE  EFFECT  OF  PRESSURE.  —  In  all  matters  pertaining  to 
melting  and  solidification,  we  are  dealing  with  a  system  of  two 
phases.  According  to  the  phase  rule  we  must  therefore  expect 
one  degree  of  freedom,  for  then  the  sum  of  phases  and  degrees  of 
freedom  will  be  three,  as  demanded  by  the  rule;  in  other  words, 
we  must  expect  that  the  melting  point  will  vary  with  a  change  in 
pressure. 

For  a  long  time  observations  did  not  appear  to  support  this 
expectation.  It  had  long  been  recognised  that  variations  in  baro- 
metric pressure  had  an  effect  on  the  boiling  point  of  water  which 
was  very  easily  observed,  but  no  effect  of  barometric  pressure 
on  the  melting  point  of  water  had  been  found.  Finally,  when 
very  much  higher  pressures  were  applied,  a  shift  in  the  melting 
point  was  observed.  It  is  only  in  the  minuteness  of  the  effect  that 
the  phenomena  differ  from  those  of  vaporization.  An  increase 
of  pressure  results  sometimes  in  a  rise,  sometimes  in  a  decrease, 
of  the  melting  point,  while  the  boiling  point  is  always  raised  by 
an  increase  of  pressure.  These  two  facts,  the  very  slight  influence 
of  pressure  and  the  possible  difference  in  direction  of  the  change, 
are  explained  as  follows: 

During  vaporization  the  volume  increases,  and  usually  by  a 
very  large  amount.  In  the  case  of  water  at  its  boiling  point  under 
atmospheric  pressure  the  vapour  occupies  about  1200  times  the 
volume  of  the  liquid.  During  melting,  however,  the  change  of 
volume  is  always  very  small.  The  volume  usually  increases  dur- 
ing melting,  but  in  some  cases,  water  especially,  the  volume  de- 
creases, for  ice  has  a  lower  density  than  water  and  floats  upon  it. 
The  influence  of  pressure  on  the  equilibrium  is  dependent  on  the 
direction  and  amount  of  this  volume  change,  and  it  is  very  great 
during  vaporization  and  always  positive,  pressure  and  tempera- 
ture rising  simultaneously.  In  the  case  of  melting,  the  influence 
of  pressure  is  small.  It  is  positive  for  most  substances,  because 


CHANGE   OF   STATE   AND   EQUILIBRIUM  83 

they  increase  their  volume  somewhat  during  melting,  but  it  is 
negative  for  water,  which  decreases  its  volume  when  it  changes 
from  a  solid  to  a  liquid.  A  pressure  increase  of  one  atmosphere 
lowers  the  melting  point  of  water  .0073°  C.  It  is  now  very  easy 
to  understand  why  the  effect  of  a  change  in  barometric  pressure  on 
the  melting  point  of  water  was  not  noticed  earlier,  since  changes  in 
barometric  pressure  are  seldom  greater  than  ^  of  an  atmosphere. 
We  have  already  used  a  vapour  pressure  line  to  express  the  re- 
lation between  vapour  pressure  and  temperature  for  a  pure  sub- 
stance. There  is  a  corresponding  melting  point  line.  Even  when 
very  great  changes  of  pressure  are  considered  this  line  will  include 
only  a  very  small  region  of  temperature  in  the  neighbourhood  of 
the  ordinary  melting  point,  for  it  is  not  possible  to  produce  and 
measure  pressures  greater  than  a  few  thousand  atmospheres.  It 
is  therefore  difficult  to  say  anything  very  definite  about  the  critical 
phenomena  which  correspond  to  the  transformation  of  a  solid 
into  a  liquid,  and  vice  versa. 

66.  SUPERCOOLING.  —  In   the   transition   from   liquid   to   solid 
phenomena  similar  to  those  of  supersaturation  often  appear,  and 
to  this  case  the  name  supercooling  is  applied.     Liquids  can  be 
cooled  below  their  point  of  solidification  without  becoming  solid, 
provided  every  trace  of  the  solid  phase  is  carefully  excluded.     It 
is   not   possible   to   carry   supercooling  very   far.      Presently   the 
metastable  condition  gives  place  to  the  labile,  and  solidification 
takes  place. 

The  reverse  phenomenon,  the  heating  of  a  substance  above  its 
melting  point  without  its  changing  into  a  liquid,  has  never  been 
observed  with  certainty.  There  is  no  general  reason  why  it  should 
not  be  possible,  but  it  is  easy  to  see  that  there  would  be  great 
difficulty  in  fulfilling  the  condition  that  every  trace  of  the  liquid 
phase  should  be  excluded. 

67.  THE  LAW  OF  THE  DISPLACEMENT  OF  EQUILIBRIUM.  —  The 
relations  just  discussed"  between  the  change  of  volume  accompany- 
ing a  change  of  state  and  the  effect  of   pressure  on  equilibrium 


84  FUNDAMENTAL   PRINCIPLES   OF  CHEMISTRY 

are  individual  cases  of  a  general  law  which  is  applicable  to  all 
equilibria  of  this  type,  and  which  is  the  most  general  expression 
of  equilibrium.  In  order  that  a  system  shall  retain  its  condition 
unchanged,  there  must  be  present  in  it  a  cause  which  brings  the 
system  back  into  its  original  condition  whenever  it  is  disturbed. 
If,  for  example,  a  heavy  mass  is  suspended  by  a  thread  it  takes  up 
a  position  of  equilbrium,  such  that  work  must  be  performed  in 
order  to  remove  it  from  this  position.  If  then  it  is  moved  in  any 
way,  an  effect  results  which  brings  the  mass  back  again  into  its 
position  of  equilibrium. 

The  equilibria  which  we  are  considering  are  of  this  same  kind. 
If  we  produce  a  change  in  our  conditions,  processes  are  induced 
which  oppose  the  force  applied.  If  the  volume  of  a  mixture  of 
water  and  ice  is  forcibly  reduced  changes  will  be  induced  which 
will  make  the  pressure  applied  as  ineffective  as  possible,  and  in 
this  case  a  process  accompanied  by  a  decrease  of  volume  will 
take  place.  A  part  of  the  ice  will  melt  because  its  volume  is  greater 
than  that  of  the  water  which  can  be  produced  from  it.  By  the 
melting  of  ice  heat  will  be  absorbed  and  the  temperature  will  drop 
until  a  new  condition  of  equilibrium  has  been  attained.  The 
higher  pressure  therefore  corresponds  to  a  lower  temperature. 
If  the  experiment  is  carried  out  with  another  substance  which 
expands  on  melting  (paraffin,  for  example),  a  decrease  in  volume 
can  only  be  brought  about  by  the  solidification  of  a  part  of  the 
substance.  Heat  is  set  free  during  this  solidification  and  the 
temperature  rises.  The  new  equilibrium  at  higher  pressure  lies 
therefore  at  higher  temperature. 

In  the  transformation  of  liquid  into  vapour  the  relations  are 
simpler,  because  the  transformation  is  always  accompanied  by 
an  increase  of  volume,  and  never  the  reverse.  This  corresponds 
to  the  second  of  the  two  cases.  Vapour  disappears  during  the  de- 
crease of  volume,  heat  is  set  free,  and  the  new  equilibrium  at  higher 
pressure  lies  at  higher  temperature. 


CHANGE   OF  STATE  AND   EQUILIBRIUM  85 

(c)  Equilibrium  between  the  three  States 

68.  THE  TRIPLE  POINT.  —  In  systems  consisting  of  two  phases 
of  a  pure  substance  there  still  remains  one  degree  of  freedom. 
We  can  therefore  make  use  of  this  by  causing  a  third  phase  to 
appear.     All  the  degrees  of  freedom  have  then  been  disposed  of, 
and  we  must  therefore  conclude  that  such  a  condition  can  only 
hold  for  a  pure  substance  at  one  single  temperature  and  one  single 
pressure,  since  there  is  no  longer  any  freedom  for  change.     Let 
us  state  a  case  of  this  sort  for  water.    If  we  have  liquid  water  and 
water  vapour,  these  can  exist  together  at  a  whole  series  of  very 
different  temperatures.     If  ice  is  to  be  present  at  the  same  time 
the  temperature  must  be  very  nearly  0°,  for,  as  we  have  seen, 
very  great  changes  in  pressure  affect  the  melting  point  only  very 
slightly.     The  condition  that  vapour  shall  also  be  present  means 
that  the  pressure  must  be  very  small,  for  water  vapour  can  only 
exist  in  the  presence  of  liquid  water  at  0°  at  a  pressure  of  0.458  cm. 
of  mercury  (see  Sec.  53).     At  this  pressure  the  melting  point  of 
ice  is  +0.0074°.     The  temperature  0°  has  been  defined  as  the 
melting  point  under  atmospheric  pressure,  and  since  a  decrease 
in  pressure  corresponds  to  a  rise  in  the  .melting  point  of  ice  of 
0.0074°  for  each  atmosphere,  the  melting  point  at  pressure  zero 

must  be  +0.0074°.    At  a  pressure  of  0.458  cm.  it  would  lie  — — 

76 

degrees  lower  than  this  point.     This  difference  is  so  small,  how- 
ever, that  the  number  0.0074°  is  practically  not  changed  by  it. 

Ice,  water,  and  water  vapour  can  therefore  exist  together  at  a 
pressure  of  0.458  cm.  and  a  temperature  +0.0074°.  Such  a 
point  at  which  three  phases  of  a  pure  substance  can  exist  together 
is  called  a  triple  point.  Every  pure  substance  has,  generally 
speaking,  such  a  point,  but  in  many  cases  our  experimental  means 
are  insufficient  to  enable  us  to  reach  it. 

69.  THE  EQUILIBRIUM  LAW.  —  One  objection  can  be  raised 
to  the  preceding  considerations,  and  it  leads  to  an  important  gen- 


86  FUNDAMENTAL   PRINCIPLES  OF  CHEMISTRY 

eralization.  It  has  been  said  that  the  vapour  pressure  of  water 
at  the  triple  point  is  0.458  cm.  But  ice  has  also  a  perfectly  definite 
vapour  pressure,  and  the  question  arises,  how  great  is  the  vapour 
pressure  of  ice  at  the  temperature  in  question  ?  It  might  evidently 
be  either  the  same  as  that  of  water  or  different  from  it. 

Let  us  assume  that  the  vapour  pressure  of  ice  is  different  from 
that  of  water  at  the  triple  point.  We  must  then  conclude  that 
equilibrium  at  the  triple  point  is  impossible  and  that  the  con- 
dition represented  by  this  point  is  not  unchangeable  with  time; 
for  if  the  vapour  pressure  of  water  were  greater  than  that  of  ice, 
water  must  evaporate  and  precipitate  as  ice.  If  the  vapour  space 
were,  at  the  beginning  of  the  experiment,  filled  with  water  vapour  at 
the  pressure  corresponding  to  that  of  the  water,  this  vapour 
will  be  supersaturated  with  respect  to  ice;  that  is,  the  vapour 
pressure  will  be  greater  than  that  corresponding  to  equilibrium 
with  ice,  and  vapour  must  then  change  into  ice  until  the  corre- 
sponding pressure  has  been  attained.  But  when  this  condition 
has  been  reached  the  vapour  space  is  filled  with  vapour  which  is 
unsaturated  with  respect  to  liquid  water  and  more  water  will 
evaporate.  If  the  temperature  is  kept  constant  all  the  water  must 
therefore  evaporate  and  change  into  ice,  and  this  means  that  water 
cannot  exist  together  with  water  vapour  and  ice.  If  the  opposite 
assumption  is  made,  that  the  vapour  pressure  of  ice  is  greater  than 
that  of  water  at  the  same  temperature,  similar  reasoning  leads  to 
the  conclusion  that  ice  cannot  exist  in  the  presence  of  water  and 
water  vapour. 

Experience  has  shown  that  it  is  possible  to  produce  a  triple 
point  which  is  independent  of  time,  and  therefore  corresponds  to 
a  true  equilibrium  condition.  The  conclusion  from  this  fact  of 
experience  is  that  at  the  triple  point  the  vapour  pressure  of  the 
solid  and  the  liquid  phase  must  be  the  same. 

This  result  can  be  given  more  general  expression.  If  the  ex- 
istence of  a  condition  of  equilibrium  has  been  proven,  it  is  always 
safe  to  conclude  that  for  every  imaginable  change  in  this  condition 


CHANGE   OF  STATE  AND   EQUILIBRIUM  87 

forces  will  be  produced  which  preclude  the  possibility  of  such  a, 
change.  If  forces  of  this  sort  did  not  obtain  for  every  possible 
way  in  which  the  change  might  take  place,  we  would  only  need 
to  so  arrange  the  system  that  the  change  could  take  place.  The 
system  will  usually  be  found  to  be  in  the  condition  required,  and 
we  can  then  conclude  from  the  fact  that  the  change  does  not  take 
place  that  forces  were  present  which  prevented  the  change.  In 
the  case  just  described  the  necessary  condition  is  the  equality  of 
the  vapour  pressures  of  the  two  coexistent  phases. 

This  entire  chain  of  reasoning  may  be  summarized  as  follows : 
A  system  which  is  in  equilibrium  in  one  sense  is  in  equilibrium  in 
every  sense. 

This  principle  has  been  most  fruitful  as  an  aid  to  the  discovery 
of  numerical  relations.  If  it  has  once  been  proven  for  any  system 
whatever  that  it  is  in  a  condition  of  equilibrium,  we  can  state  the 
direction  in  which  the  equilibrium  will  change  for  any  given  change 
of  the  system,  and  we  can  then  be  sure  that  the  determining  factors 
will  so  equalize  one  another  that  the  process  will  not  take  place. 
Each  way  therefore  leads  to  an  equation  between  these  determin- 
ing factors,  and  through  this  to  a  numerical  relation  between  the 
corresponding  properties.  We  shall  later  have  occasion  to  illus- 
trate this  rather  abstract  reasoning  by  further  examples  of  its 
application. 

In  the  application  of  this  fundamental  principle  it  must  be  re- 
membered that  relations  are  not  to  be  derived  in  a  logical  or 
mathematical  way  without  recourse  to  experience.  The  experience 
which  must  always  be  obtained  is  the  proof  that  a  real  equilibrium 
exists.  This  means  that  we  must  make  observations  on  the  system 
and  show  that  it  does  not  change  its  condition  under  constant 
temperature  and  pressure.  The  individual  principles  derived  by 
means  of  this  fundamental  law  are  therefore  just  so  many  expres- 
sions of  the  experimental  facts  about  the  equilibrium.  The  fact 
of  the  existence  of  equilibrium  is  the  general  statement  which  in- 
cludes in  itself  all  of  these  separate  principles. 


88 


FUNDAMENTAL   PRINCIPLES   OF  CHEMISTRY 


70.  THE  VAPOUR  PRESSURE  CURVES  AT  THE  TRIPLE  POINT.  - 
This  reasoning  can  be  reversed  and  leads  to  the  conclusion  that 
outside  the  triple  point  the  vapour  pressure  of  ice  and  water  must 
be  different,  for  outside  of  this  point  ice  and  water  are  not  in 
equilibrium  in  the  presence  of  water  vapour.  At  a  lower  tempera- 
ture water  freezes  and  changes  into  ice,  and  at  a  higher  tempera- 
ture ice  melts  and  changes  into  water.  From  the  fact  that  water 
is  unstable  and  cannot  exist  in  the  presence  of  ice  at  a  lower  tem- 
perature, but  changes  into  ice,  we  must  conclude  that  the  vapour 
pressure  of  water  is  the  greater.  When  water  and  ice  are 
placed  together  in  a  space  containing  water  vapour,  but  not  in 
actual  contact,  and  at  a  temperature  below  +  0.0074°,  the  water 
will  distil  over  to  the  ice  because  of  its  higher  vapour  pressure, 
and  this  will  continue  until  all  the  water  has  evaporated  and 
changed  into  ice.  Experiment  has  confirmed  this  conclusion. 


TEMPERA  TURE 
FIG.  3. 

On  the  other  hand,  ice  above  +0.0074°  has  a  higher  vapour  pres- 
sure than  water,  and  under  the  same  conditions,  where  actual 
contact  is  excluded,  ice  will  evaporate  and  precipitate  as  water 
until  all  the  ice  has  disappeared.  These  considerations  can  all 
be  indicated  by  plotting  the  vapour  pressure  lines  of  ice  and 
water  as  they  change  with  temperature,  and  Fig.  3  is  a  diagram 


CHANGE  OF   STATE   AND   EQUILIBRIUM  89 

of  this  sort.  The  lines  for  water  and  ice  are  plotted  in  the  same 
units  and  they  cut  one  another  at  +0.00074°,  the  point  where  the 
two  vapour  pressures  are  the  same.  What  has  been  explained 
for  water  in  its  various  states  holds  for  all  other  pure  substances, 
as  far  as  their  triple  points  have  been  attained  and  measured. 

(rf)   The  Equilibrium  Solid-Solid 

71.  ALLOTROPISM.  —  A  given  substance  can  have  only  one  form 
as  a  gas  or  as  a  liquid,  but  the  number  of  solid  forms  in  which  it 
can  exist  is  not  limited.    Whenever  a  substance  has  several  solid 
states  these  have  the  same  relation  to  each  other  as  the  states  in 
general.    There  is  a  definite  temperature  at  which  a  solid  substance 
melts,  and  there  is  also  a  definite  temperature  at  which  one  solid 
form  of  a  substance  changes  into  another  solid  form. 

This  can  be  seen  very  clearly  in  the  case  of  mercuric  iodide.  At 
ordinary  temperatures  this  is  a  scarlet  substance  which  retains  its 
colour  without  much  change  as  the  temperature  is  raised  until  126° 
is  reached.  If  it  is  heated  above  this  point  its  red  colour  disappears, 
and  a  sulphur-yellow  colour  takes  its  place.  At  the  same  point  all 
of  its  other  properties  change;  its  crystalline  form,  its  density,  its 
hardness,  etc.,  take  on  new  values.  If  the  temperature  is  lowered 
the  transformation  takes  place  in  the  opposite  sense.  The  red  sub- 
stance is  produced  from  the  yellow,  and  all  the  original  properties 
appear  again  unchanged. 

This  transformation  is  one  which  corresponds  to  an  ordinary 
change  of  state,  and  more  exact  investigation  has  shown  that  this 
change  is  in  no  way  different  from  the  one  previously  described. 
Transformations  of  this  sort,  which  are  called  allotropic  changes, 
can  therefore  be  included  among  general  changes  of  state.  It  has 
already  been  stated  that  changes  of  this  sort  do  not  appear  in 
liquids  and  gases,  and  it  can  be  said,  in  general,  that  any  sub- 
stance may  have  one  gaseous,  one  liquid,  and  several  solid  forms. 

72.  THE  INFLUENCE  OF  PRESSURE.  —  At  the  temperature  at 
which  the  allotropic  transformation  of  one  solid  form  into  another 


90  FUNDAMENTAL  PRINCIPLES  OF  CHEMISTRY 

takes  place  the  two  forms  can  exist  together.  Above  or  below  this 
temperature,  which  is  called  the  transition  temperature,  only  one  or 
the  other  of  the  two  forms  is  stable.  As  in  the  case  of  the  boiling 
and  the  melting  points  we  must  expect  that  the  allotropic  transi- 
tion point  will  be  variable  with  pressure.  Transformations  of  this 
sort  are  in  general  accompanied  by  only  a  very  small  change  of 
volume.  We  may,  therefore,  expect  that  the  effect  of  pressure  on 
the  transition  temperature  will  be  only  a  slight  one.  As  in  the  case 
of  boiling  and  melting,  heat  is  always  absorbed  when  the  substance 
changes  from  the  condition  which  is  stable  at  the  lower  temper- 
ature into  that  which  is  stable  at  the  higher  temperature.  Pres- 
sure has  therefore  exactly  the  same  influence  on  the  transition  point 
as  on  the  melting  point.  An  increase  of  pressure  changes  the 
transition  point  in  such  a  way  that  the  form  possessing  the  smaller 
volume  is  most  stable  at  higher  temperatures.  If  then  the  form 
which  belongs  in  the  upper  region  of  temperature  has  the  smaller 
volume,  the  transition  temperature  will  be  lowered  by  an  increase 
of  pressure.  If  this  form  has  the  greater  volume,  an  increase  of 
pressure  results  in  a  rise  of  transition  temperature.  The  effect  of 
pressure  is  very  small  in  either  case,  but  it  has  been  measured,  and  the 
results  have  been  in  agreement  with  the  predictions  of  the  theory. 
73.  THE  PHENOMENA  OF  SUSPENDED  TRANSFORMATION.  - 
The  phenomena  of  allotropism  are  in  some  respects  different  from 
those  of  boiling  and  melting.  Phenomena  similar  to  those  of  super- 
saturation  are  very  common  among  the  allotropic  forms,  and  those 
which  are  unstable  under  existing  conditions  can,  nevertheless,  ex- 
ist for  a  very  long  time,  even  in  contact  with  the  more  stable  form, 
transformation  taking  place  very  slowly  indeed.  It  is  for  this  rea- 
son that  such  unstable  forms  can  very  often  be  observed  and  in- 
vestigated without  any  sign  of  their  instability  becoming  evident. 
The  phase  rule  says,  to  be  sure,  that  in  general,  and  under  given 
conditions  of  pressure  and  temperature,  only  one  single  form  can 
exist.  The  existence  of  two  forms  is  connected  with  a  series  of 
simultaneous  values  of  pressure  and  temperature,  while  three  can 


CHANGE   OF  STATE  AND   EQUILIBRIUM  91 

only  exist  at  one  single  temperature.  As  far  as  this  is  concerned, 
we  should  only  find  two  allotropic  forms  of  a  substance  existing 
near  a  transition  temperature,  and  only  one  single  solid  form 
should  be  stable  at  that  point.  This  is  far  from  being  the  case. 
We  recognize,  for  example,  three  solid  forms  of  carbon,  —  diamond, 
graphite,  and  coal;  and  there  is  no  apparent  tendency  of  two  of 
these  forms  to  disappear  with  formation  of  the  third.  We  know 
phosphorus  in  two  forms,  one  red  and  one  yellow,  and  both  of  these 
can  be  kept  for  a  very  long  time  at  ordinary  temperatures  without 
either  of  them  changing  into  the  other.  In  this  case,  however,  we 
do  find  that  yellow  phosphorus  tends  to  change  into  the  red  form, 
which  is  the  more  stable  of  the  two,  but  the  transformation  takes 
place  very  slowly  indeed. 

The  important  fact  is  that  transformations  of  this  sort  never  take 
place  instantaneously,  but  always  need  a  certain  time  for  their 
completion.  In  those  changes  of  state  which  we  have  previously 
described  this  time  is  short,  and  melting,  for  example,  takes  place 
with  a  velocity  only  dependent  on  the  rate  at  which  the  necessary 
heat  is  supplied.  The  time  of  transformation  among  allotropic 
substances  is,  in  -general,  much  greater,  and  in  some  cases  so  great 
that  a  measurable  transformation  has  never  been  observed: 

Cases  of  this  sort  can  be  arranged  in  a  continuous  series  with 
those  where  transformation  takes  place  at  a  measurable  rate,  and 
often  a  mere  increase  of  temperature  (which  usually  means  a  very 
greatly  increased  velocity  of  transition)  results  in  the  production  of 
a  measurable  transition  velocity.  WTe  are  therefore  justified  in  as- 
suming that  in  these  cases  also  the  transformation  actually  takes 
place,  though  too  slowly  to  come  within  range  of  our  observation. 
Such  an  assumption  oversteps  the  bounds  of  experience,  however, 
and  we  only  use  it  because  we  know  no  reason  why  such  cases 
should  be  in  any  way  different  from  the  ordinary  ones. 

74.  THE  STEP  BY  STEP  LAW.  —  Those  forms  of  a  substance 
which  are  unstable  in  contact  with  another  form  of  the  same  sub- 
stance can  be  brought  within  the  range  of  observation  in  two  ways. 


92  FUNDAMENTAL  PRINCIPLES  OF  CHEMISTRY 

One  of  these  is  to  produce  the  substance  in  a  form  which  is  stable, 
and  then  to  so  vary  temperature  or  pressure,  or  both,  that  the 
limit  of  stability  is  overstepped.  If  the  new  phase  which  would 
be  stable  in  this  new  region  is  kept  out,  the  less  stable  form  persists 
for  a  shorter  or  longer  time  according  to  conditions,  and  some- 
times even  for  an  unlimited  time.  We  have  already  termed  such  a 
condition  metastable. 

There  are,  however,  forms  which  have  no  region  of  stability 
within  the  limits  of  pressure  and  temperature  which  we  can  attain. 
Yellow  phosphorus  is  a  form  of  this  kind.  As  far  as  we  can  find 
out  red  phosphorus  is  far  more  stable  than  yellow  phosphorus  under 
all  conditions.  In  spite  of  this  fact  yellow  phosphorus  is  not  only 
better  known  than  red,  but  it  was  also  discovered  at  a  much  earlier 
date.  And  in  the  chemical  manufacture  of  phosphorus  it  is  always 
the  yellow  that  appears  first  and  never  the  red.  In  this  case  it  is 
impossible  that  this  form  has  remained  present  in  spite  of  varia- 
tion in  the  conditions  of  stability.  There  must  be  a  reason  why 
such  unstable  forms  appear  in  spite  of  the  fact  that  more  stable 
forms  are  possible  under  the  same  conditions.  We  have  here  in 
fact  a  general  law  of  nature.  WThen  one  form  of  a  substance  is 
transformed  into  another,  the  first  form  to  appear  is  not  the  one 
which  would  be  the  most  stable  under  the  new  conditions.  Those 
forms  appear  first  which  are  more  stable  than  the  form  just  left, 
but  which  are  the  least  stable  among  all  the  possible  stable  forms. 
If  the  various  forms  of  a  substance  which  can  exist  under  given 
conditions  are  labelled  1,  2,  3,  4,  in  the  order  of  stability,  1  being 
the  least  stable  form,  then  when  the  substance  voluntarily  leaves 
the  state  1  the  most  stable  form  4  is  not  the  one  which  will  appear. 
The  form  2  will  appear  first,  and,  depending  on  whether  this  is 
metastable  or  labile,  it  will  either  remain  unchanged  or  pass  over 
into  3.  If  there  is  a  form  4,  which  is  more  stable  than  3  under  the 
same  conditions,  form  3  will  form  first  from  2  and  then  afterwards 
change  into  4.  A  very  great  number  of  facts  are  known  which 
confirm  this  law.  If,  for  example,  water  is  placed  in  a  small  glass 


CHANGE  OF  STATE  AND   EQUILIBRIUM  93 

retort,  the  air  driven  out  by  boiling,  and  the  tube  then  sealed, 
liquid  water  can  be  obtained  as  a  distillate  when  the  neck  of  the  re- 
tort is  cooled,  even  when  a  freezing  mixture  at  a  temperature  of 
—  5°  to  —10°  is  used  in  the  condensation.  Ice  is,  of  course,  the 
more  stable  form  at  this  temperature,  but  ice  does  not  appear  first. 
Liquid  water  is  the  first  form  to  appear,  and  it  is  more  stable  than 
water  vapour  under  the  conditions  existing,  but  less  stable  than 
ice.  In  just  the  same  way,  when  mercuric  iodide  is  sublimed  in  a 
vacuum  at  a  temperature  below  126°,  the  yellow  form  appears  first, 
although  the  red  form  is  more  stable.  And  this  is  the  reason  why 
phosphorus  condenses  from  the  form  of  vapour  first  of  all  in  the 
unstable  yellow  form  which  is  then  transformed  under  proper  con- 
ditions into  the  more  stable  red  form.  By  proper  conditions  we 
mean,  in  this  case,  a  high  enough  temperature  to  give  a  measurable 
value  to  the  velocity  of  transition. 

In  this  way  we  very  often  obtain  a  knowledge  of  forms  which 
have  no  region  of  stability  whatever.  If  these  forms  are  metastable 
they  can  be  kept  for  any  length  of  time  without  changing  into  the 
more  stable  forms,  if  they  are  protected  from  contact  with  the 
latter.  If  they  are  labile  forms  they  can  only  be  kept  for  a  certain 
time,  but  this  time  may  take  on  the  appearance  of  eternity  because 
of  a  very  low  transition  velocity,  and  this  case  is  not  at  all  an  un- 
.  common  one. 

75.  THE  VAPOUR  PRESSURE  OF  ALLOTROPIC  FORMS.  —  The 
matter  of  stability  is  one  of  great  importance  in  the  study  of  allo- 
tropic  forms.  It  is  very  often  difficult  to  decide  questions  of  sta- 
bility by  direct  observation,  and  it  is  a  question  of  great  importance 
whether  there  is  not  another  independent  means  of  determining 
stability.  This  question  can  be  answered  in  the  affirmative.  There 
are  several  means,  and  the  simplest  is  found  in  the  measurement  of 
vapour  pressure. 

Let  us  consider  two  different  forms  of  a  substance  brought  into 
an  empty  space  in  contact  with  its  vapour.  Two  cases  are  possible. 
The  vapour  pressures  of  the  two  forms  may  be  the  same,  and  then 


94  FUNDAMENTAL   PRINCIPLES   OF  CHEMISTRY 

the  two  forms  will  be  in  equilibrium,  and  neither  will  increase  in 
amount  at  the  expense  of  the  other.  In  accordance  with  the  prin- 
ciple already  given,  that  any  system  which  is  in  equilibrium  in  one 
way  must  be  in  equilibrium  in  all  ways,  two  forms  which  are  in 
equilibrium  with  respect  to  their  vapour  will  also  remain  without 
influence  on  each  other  when  they  are  brought  into  direct  contact. 
The  other  case  is  that  in  which  the  two  vapour  pressures  are  dif- 
ferent. Then  the  two  forms  cannot  be  in  equilibrium,  and  the  one 
with  the  lower  vapour  pressure  must  be  the  more  stable.  Under 
the  conditions  given  both  forms  will  send  out  vapour.  As  soon  as 
the  vapour  pressure  corresponding  to  the  more  stable  form  is 
reached,  this  form  will  no  longer  evaporate,  but  the  other  form  will 
continue  to  change  into  vapour.  The  vapour  will  therefore  be- 
come supersaturated  with  respect  to  the  first  form  and  precipita- 
tion will  occur  upon  this.  The  vapour  cannot  then  be  saturated 
with  respect  to  the  second  form  and  the  latter  must  continue  to 
evaporate.  It  is  evident  that  the  only  way  in  which  a  stationary 
condition  can  be  attained  is  that  the  form  with  the  greater  vapour 
pressure  shall  completely  evaporate,  leaving  only  the  form  with 
the  lower  vapor  pressure  in  contact  with  its  vapour. 

Similar  reasoning  can  evidently  be  applied  to  any  process  which 
leads  to  the  production  of  a  third  phase  common  to  the  two  forms. 
In  case  equilibrium  does  not  exist  the  transformation  through  the. 
common  third  phase  must  evidently  take  place  in  a  definite  di- 
rection. The  case  just  discussed  is,  however,  the  simplest  one; 
and  in  general  the  others  require  the  presence  of  a  second  sub- 
stance. From  this  reasoning  we  must  conclude  that  at  the  transi- 
tion point  where  two  allotropic  forms  are  in  equilibrium  with  each 
other,  the  vapour  pressure  of  each  must  be  the  same,  and  this 
agrees  perfectly  with  the  conclusions  reached  by  a  consideration  of 
the  vapour  pressures  of  a  substance  in  the  solid  and  the  liquid 
states.  The  same  conclusion  is  applicable  to  the  melting  point, 
which  is  analogous  to  the  transition  point,  and  at  any  point  out- 
side the  melting  point  the  less  stable  form  has  the  higher  vapour 


CHANGE   OF  STATE  AND   EQUILIBRIUM  95 

pressure.     The  reasoning  used  in  connection  with  Fig.  3  can  be 
applied  directly  to  allotropic  forms. 

Some  allotropic  forms  have  no  transition  points  which  we  have 
been  able  to  find.  In  this  case  one  of  the  forms  is  unstable  as  com- 
pared with  the  other  over  the  entire  region  known  to  us  (this  region 
is  bounded  in  the  direction  of  higher  temperatures  by  the  melting 
point).  The  unstable  form  in  this  case  always  has  a  higher  vapour 
pressure  than  the  stable  form,  and  no  point  is  known  where  the 
two  vapour  pressures  are  the  same. 


CHAPTER  V 

SOLUTIONS 

76.  GENERAL  CONSIDERATIONS.  —  Solid  bodies  which  we  find 
in  nature,  or  prepare  artificially,  obey,  in  general,  the  substance 
law  expressed  in  Sec.  7.  They  have  perfectly  definite  forms, 
sharply  distinguished,  and  unconnected  in  any  way.  Liquids  and 
gases,  however,  often  show  deviations  from  this  law.  Among 
them  we  find  substances  possessing  all  possible  values  for  their 
properties  between  certain  limits,  and  in  place  of  sharply  differ- 
entiated individual  forms  we  find  an  unlimited  number  of  inter- 
mediate ones. 

Such  intermediate  forms  are  called  solutions.  They  are  very 
frequent  in  nature,  and  they  are  easy  to  make  by  bringing  together 
or  mixing  various  gases  or  liquids.  Under  these  circumstances 
solids  form  inhomogeneous  mixtures  in  which  the  components 
can  be  distinguished  either  directly  or  by  microscopic  examina- 
tion, and  out  of  which  the  constituents  can  be  separated  by  me- 
chanical means.  When  gases  are  brought  together  they  always 
form  homogeneous  substances,  and  liquids  very  often  act  in  the 
same  way.  In  this  case  it  is  impossible  to  distinguish  any  con- 
stituents of  the  mixture,  and  it  is  impossible  to  separate  them  by 
mechanical  means  into  the  substances  from  which  they  were  made. 
The  properties  of  these  solutions  are  different  from  those  of  the 
constituents  from  which  they  were  produced,  and  their  formation 
therefore  comes  under  the  head  of  a  chemical  process. 

There  has  been  a  long  discussion  over  the  question  whether 
solution  is  a  physical  or  a  chemical  process.  Differences  of  opinion 
on  this  point  must  remain  unsettled  as  long  as  no  definite  agree- 

96 


SOLUTIONS  97 

ment  about  the  use  of  the  word  has  been  reached.  We  have 
already  decided  that  chemical  processes  are  those  in  which,  from 
given  substances,  others  with  other  properties  result,  and  in  ac- 
cordance with  this  definition  the  process  of  solution  must  be  char- 
acterized as  a  chemical  one.  This,  of  course,  does  not  mean  that 
we  have  predetermined  anything  about  the  relation  between  a 
solution  and  its  constituents,  nor  does  it  mean  that  we  have  said 
anything  about  the  question  whether  or  not  the  constituents  are 
to  be  considered  as  existing  in  the  solution. 

The  process  of  solution  is  to  be  distinguished  from  a  change  in 
state  especially  by  the  fact  that  at  least  two  different  substances 
are  always  necessary  to  form  a  solution.  By  a  change  in  state,  or 
still  more  generally  by  the  formation  of  a  new  phase,  solutions 
can  always  be  separated  into  substances  which  obey  the  general 
law  of  substances.  Those  which  obey  this  law  we  have  called 
pure  substances,  and  these  are  the  ones  whose  transformation  into 
other  states  can  be  carried  out  at  constant  temperature  and  con- 
stant pressure.  Any  solution  is  therefore  completely  characterized 
by  stating  the  nature  and  proportion  of  the  pure  substances  of 
which  it  is  composed,  or  into  which  it  can  be  separated.  The 
formation  and  the  splitting  up  of  a  solution  are  reversible.  If,  for 
example,  a  solution  has  been  made  up  of  one  third  of  a  substance 
A  and  two  thirds  of  a  substance  B,  this  same  solution  can  always 
be  broken  up  so  that  one  third  A  and  two  thirds  B  result,  assum- 
ing, of  course,  that  it  is  possible  to  make  a  complete  separation. 

There  are  therefore  solutions  containing  2,  3,  or  more  constit- 
uents, and  these  are  called  binary,  ternary,  etc.,  solutions.  We 
shall  have  to  do  almost  entirely  with  binary  solutions,  for  among 
them  the  simplest  relations  obtain. 

77.  KINDS  OF  SOLUTIONS.  —  A  solution  may  be  gaseous,  liquid, 
or  solid.  It  has  been  said  that  solid  substances  generally  obey 
the  law  of  substances,  and  this  means  that  they  do  not,  in  general, 
form  solutions.  An  exception  must  be  made  to  this  statement, 
for  solid  solutions  do  occur,  but  comparatively  very  rarely,  and 
7 


98  FUNDAMENTAL  PRINCIPLES  OF  CHEMISTRY 

they  are  usual  only  between  solid  substances  which  are  similar 
to  each  other.  When  we  are  dealing  with  gaseous  and  liquid  sub- 
stances we  must  always  bear  in  mind  that  they  may  be  solutions, 
but  when  we  are  dealing  with  solids  it  is  very  much  more  probable 
that  they  are  pure  substances.  A  chemist  who  wishes  to  produce 
pure  substances  always  tries  to  get  them  into  the  solid  state  if 
possible.  This  is  usually  brought  about  by  lowering  the  tempera- 
ture, but  in  the  course  of  our  discussion  on  the  properties  of  solu- 
tions we  shall  learn  about  other  means  of  attaining  the  same  end. 

Gaseous  solutions  are  produced  when  two  gases  are  brought 
together.  They  can  also  result  when  a  gas  comes  in  contact  with 
a  liquid  or  a  solid,  provided  the  latter  substance  vaporizes.  Cases 
where  a  gaseous  solution  is  formed  by  the  interaction  of  liquid  or 
solid  bodies  are  not  absolutely  excluded,  but  such  a  special  set  of 
conditions  are  necessary  that  we  shall  not  consider  this  case  for 
the  present.  Whenever  cases  of  this  sort  appear  possible  in  the 
course  of  our  later  discussion  special  attention  will  be  called  to 
them. 

78.  SOLUTIONS  OF  GASES.  —  Gases  have  the  property  of  form- 
ing solutions  in  all  proportions  and  on  every  occasion.  Whenever 
any  two  or  more  gases  are  brought  together  in  any  proportions 
whatever,  the  immediate  consequence  is  always  the  formation  of 
a  homogeneous  gaseous  substance  from  all  of  these  constituents. 

Cases  are  not  at  all  rare  in  which  liquid  or  solid  bodies  are  pro- 
duced by  the  interaction  of  gases.  A  chemical  reaction  in  the 
narrower  sense  of  the  word  takes  place  which  leads  to  the  forma- 
tion of  a  new  pure  substance.  This  process  can  be  considered 
as  taking  place  after  the  mutual  solution  of  the  gases  involved, 
and  such  a  process  is  characterized  by  the  appearance  of  heat, 
light,  or  some  other  form  of  energy.  The  process  of  solution  takes 
place  among  gases  without  any  change  of  energy,  and  therefore 
without  any  change  in  temperature  and  without  the  emission  of 
light.  For  the  present  we  shall  confine  ourselves  to  these  cases  in 
which  subsequent  chemical  phenomena  do  not  appear. 


SOLUTIONS  99 

79.  DIFFUSION.  —  When  two  different  gases  are  placed  in  the 
same  vessel  they  arrange  themselves  first  of  all  in  the  order  of  their 
density,  the  heavier  gas  passing  to  the  lower  part  of  the  vessel  and 
the  lighter  gas  occupying  the  upper  part.     This  state  of  things 
does  not  continue,  and  after  a  longer  or  shorter  time,  varying  with 
the  nature  of  the  gas,  the  temperature,  and  the  shape  of  the  vessel, 
the  two  gases  will  be  found  equally  distributed  through  the  entire 
vessel.     We  have  already  learned  that  any  single  gas  fills  com- 
pletely any  vessel  in  which  it  is  placed.     It  is  evident  from  what 
we  have  just  said  that  a  gas  exhibits  the  same  property  even  though 
the  vessel  is  already  filled  with  another  gas.     In  the  case  of  an 
empty  vessel    there  is,   however,    this   difference:    A  gas   when 
placed  in  the  vessel  fills  it  very  rapidly,  almost  instantaneously, 
while  the  equalization  takes  place  very  slowly  when  another  gas 
is  already  present  in  the  vessel.    The  equalization  can  be  accel- 
erated by  mixing  the  two  gases  mechanically,  as,  for  example,  by 
moving  a  solid  body  back  and  forth  in  the  vessel;    but  mutual 
penetration   results  even   though   mechanical   mixing  is   entirely 
avoided.    In  this  case  it  may  take  days  or  weeks  for  vessels  of  some 
size  to  become  uniformly  filled,  while  the  same  result  could  be 
obtained  in  a  few  seconds  by  mechanical  agitation.    By  mechanical 
aid  the  distance  which  the  gases  have  to  travel  to  produce  a  homo- 
geneous mixture  is  very  much  shortened.    The  actual  solution,  how- 
ever, results  from  the  mutual  penetration  of  the  two  gases,  which 
is  called  diffusion.     If  solution  has  once  been  completed  between 
two  or  more  gases,  these  gases  never  voluntarily  separate  again. 
The  denser  constituent  of  a  gas  solution  does  not  gather  at  the 
bottom  of  the  vessel,  leaving  the  lighter  constituent  in  the  upper 
part.     The  condition  of  solution  is  therefore  one  which  is  volun- 
tarily assumed  by  several  gases  when  they  are  brought  together 
in  the  same  space,  and  it  is  a  state  which  they  do  not  voluntarily 
leave.    It  is  therefore  a  condition  of  comparative  stability. 

80.  THE  APPLICABILITY  OF  THE  GAS  LAWS.  —  Solutions  of 
gases  behave  exactly  like  pure  gases  toward  changes  in  pressure 


100  FUNDAMENTAL  PRINCIPLES  OF  CHEMISTRY 

and  temperature.  The  properties  described  in  Sections  32-35 
therefore  afford  no  means  of  discriminating  between  pure  gases 
and  solutions  of  gases.  But  gas  solutions  do  not  behave  like  pure 
gases  when  they  are  transformed  into  liquids  or  solids  by  lowering 
the  temperature  or  raising  the  pressure.  The  transformation  in 
the  case  of  pure  gases  can  be  carried  out  completely  at  constant 
values  of  temperature  and  pressure.  In  the  case  of  gas  solutions 
a  range  of  temperatures  and  pressures  more  or  less  considerable 
in  extent  must  be  passed  over  between  the  point  where  the  new 
phase  begins  to  separate  and  the  point  where  the  transformation 
is  ended.  This  general  fact  has  already  been  used  in  Sec.  48  in 
our  preliminary  characterization  of  solutions. 

81.  PARTIAL  PRESSURE.  —  When  two  gases  at  the  same  pres- 
sure are  placed  in  a  vessel  which  they  completely  fill,  they  first 
take  up  positions  above  each  other  in  the  order  of  their  density, 
and  mixture  and  solution  take  place  afterward.  Suppose  that 
the  common  pressure  is  p  and  the  volumes  v1  and  v2.  If  the  two 
gases  are  now  brought  into  solution,  either  by  mixing  them  mechan- 
ically or  by  waiting  for  their  complete  diffusion,  it  will  be  found 
that  the  pressure  p  does  not  change.  Each  of  the  two  gases  has 
changed  its  volume,  for  each  now  fills  the  whole  volume  of  the 
vessel,  that  is,  vl+v2.  The  pressure  must  have  experienced  a 
corresponding  change,  for,  as  observation  shows,  the  two  gases 
together  now  exercise  the  same  pressure  as  was  previously  exer- 
cised by  each  separately. 

This  shows  the  applicability  of  Boyle's  Law  for  the  case  of 
gaseous  solutions.  For  the  first  gas  the  original  volume  was  vlf 
the  final  volume  was  vl  +  v2,  and  the  formula  would  be  pv^  =  p1 
(v1  +  v2),  pt  indicating  the  unknown  pressure  exercised  by  the 

gas  over  the  whole  volume.     From  this  we  obtain  p<  = 


In  a  precisely  similar  way  we  obtain  for  the  final  pressure  of  the 
two  gases  p2  = 


SOLUTIONS  101 

Addition   of   the   two   equations    gives    Pi  +  P2  =  p>    and    this 
means  that  in  any  solution  of  two  gases  we  can  ascribe,  its  owir, 
pressure  to  each  gas  which  is  present,  and  that  this,  pressure  ,will 
be  the  same  as  that  which  the  gas  would  exerf  if'  it:  -wfi^e  pF'e#<?rPb 
alone  in  the  vessel.     This  pressure  is  called  the  partial  pressure 
of  the  gas,  and  if  the  partial  pressures  so  calculated  for  each  gas 
are  added  together,  the  sum  is  the  pressure  actually  exerted  by 
the  gas  solution. 

If  we  eliminate  the  pressure  p  from  the  two  equations  we  ob- 
tain the  relation  —  =  — ,  which  indicates  that  the  partial  pressures 
p*     v2 

are  in  the  same  relation  as  the  volumes  which  the  two  gases 
would  have  occupied  at  the  same  pressure  before  being  mixed 
together. 

It  follows  again  that  the  density  of  a  gas  solution  is  equal  to 
the  sum  of  the  densities  which  would  be  possessed  by  its  con- 
stituents, measured  in  terms  of  the  partial  pressures  and  the  total 
volume,  for  the  density  of  each  constituent  before  solution  has 
the  same  relation  to  its  density  in  the  whole  volume  after  solution 
as  the  original  volume  has  to  the  total  volume.  The  partial  pres- 
sures are  in  the  same  proportion,  and  since  the  sum  of  the  partial 
pressures  is  equal  to  the  total  pressure,  the  sum  of  the  partial 
densities,  calculated  from  the  partial  pressures,  is  equal  to  the 
total  density. 

If  the  same  calculation  is  carried  out  for  three  or  more  gases 
a  corresponding  result  will  be  obtained.  The  pressure  of  a  gas 
solution  is  therefore  always  the  sum  of  the  partial  pressures  of  the 
constituents  of  the  solution. 

82.  THE  GAS  CONSTANT  AS  APPLIED  TO  SOLUTIONS.  —  Ex- 
perience has  also  shown  that  the  coefficient  of  expansion  of  a  gas 
solution  is  the  same  as  that  of  a  pure  gas.  This  is  to  be  expected, 
for  the  coefficient  of  expansion  has  been  shown  to  be  independent 
of  the  nature  of  the  gas  (see  Sec.  33). 


102  FUNDAMENTAL   PRINCIPLES  OF  CHEMISTRY 

PV 

We  can  therefore  write  the  expression  —=-  =r  for  a  gas  solu- 
tion, and  this  expression  will  be  independent  of  pressure  and  tem- 
^ejr-atiii'eV  ;  The  temperature  T  and  the  volume  V  are  common 
to  all  the  constituents  of  the  solution,  but  each  possesses  its  own 
partial  pressure.  The  partial  pressures  are  given  by  the  relation 

p  =  p1+p2+p3 ,  and  there  will  be  as  many   members  as 

there  are  different  gases  which  have  taken  part  in  the  formation  of 
the  solution.  If  the  values  of  r,  which  are  calculated  from  the  partial 
pressures  of  the  individual  gases,  are  called  r19  r2,  r3,  etc.,  we  have 

a  set  of  equations  ^~  =  rlf  ^~-  =  r2,  etc.    By  addition  we  obtain 

v  pv 

(Pi  +  ?2  +  PS )  ™  —  ri  +  rz  +  r3 >  and  since   ~  =  r,  we 

±  L 

have  rv  +  r2  +  r3 =r.     This  means  that  the  gas  constant  r 

for  a  gas  solution  can  be  regarded  as  the  sum  of  the  gas  con- 
stants of  the  constituents,  when  these  are  calculated  in  terms  of 
the  partial  pressures. 

The  law  of  partial  pressures  was  discovered  by  John  Dalton, 
and  he  expressed  it  by  saying  that  gases  exert  no  pressure  on  each 
other.  He  was  led  to  this  by  the  facts  of  diffusion,  for  this  showed 
that  a  gas  is  not  hindered  in  its  expansion  into  a  given  space  by 
the  fact  that  this  space  is  already  occupied  by  another  gas.  The 
fact  that  gases  which  have  not  been  mechanically  agitated  can 
exist  one  over  the  other  for  a  time  shows  that  they  do  exert  a  pres- 
sure on  one  another.  It  is  therefore  better  to  avoid  this  some- 
what misleading  expression  for  the  behaviour  of  gas  solutions, 
and  to  use  the  law  of  partial  pressures  as  the  more  correct  expres- 
sion of  their  behaviour.  The  experiment  described  in  Sec.  81, 
which  showed  that  when  two  or  more  gases  pass  from  the  state  of 
a  mixture  into  that  of  a  solution  no  energy  is  given  out,  is  the 
most  direct  expression  for  the  behaviour  of  gases  during  solution, 
and  the  equation  r=r1+r2-f is  the  most  general  expres- 
sion for  the  thermal  and  mechanical  relation  between  a  gas 
solution  and  its  constituents. 


SOLUTIONS  103 

83.  OTHER  PROPERTIES  OF  GAS  SOLUTIONS.  —  As  far  as  other 
properties  are  concerned,  gas  solutions  and  their  constituents  are 
connected  by  a  relation  very  similar  to  the  one  just  described. 
Every  property  of  a  gas  solution  can,  in  general,  be  represented  as 
the  sum  of  the  properties  of  its  constituents,  if  these  constituents 
are  considered  as  occupying  the  total  volume  of  the  solution,  and 
as  being  homogeneously  distributed.  This  is  true  of  colour,  index 
of  refraction,  electrical  properties,  etc. 

The  properties  of  gas  solutions  are  therefore  simply  the  sum  of 
the  properties  of  the  constituents.  This  is  the  only  kind  of  solu- 
tion where  a  calculation  of  this  sort  is  possible.  Liquid  solutions 
(and  solid  solutions  as  far  as  we  know  anything  about  them)  do 
not  follow  this  rule,  and  the  properties  of  these  solutions  are  dif- 
ferent from  those  calculated  from  the  properties  of  the  constituents 
by  the  rule  of  mixtures.  In  this  respect  gas  solutions  behave  like 
mechanical  mixtures.  This  suggests  immediately  that  the  only 
change  produced  when  two  gases  are  dissolved  in  each  other  is  one 
of  volume.  No  error  results  when  the  properties  of  a  gas  solution 
are  calculated  from  those  of  its  constituents,  and  the  assumption 
that  pure  gases  exist  "  as  such  "  in  a  gas  solution  has  a  perfectly 
clear  meaning  when  taken  in  this  connection. 

The  properties  of  a  gas  solution  vary  continuously  with  its  com- 
position. It  is  therefore  said  that  these  properties  are  continuous 
functions  of  the  composition  of  the  solutions.  If  an  indefinitely 
small  amount  of  one  pure  gas  is  added  to  a  large  amount  of  another, 
the  properties  of  the  second  gas  are  changed  by  an  infinitesimal 
amount.  Since  there  is  no  difficulty  in  bringing  together  gases  in 
any  desired  proportion,  the  properties  of  a  solution  may  be  given 
any  desired  value  between  those  of  its  constituents.  Between  two 
solutions  of  different  composition  it  is  always  possible  to  prepare 
any  desired  number  of  other  solutions  whose  composition  lies  be- 
tween these  limits,  and  corresponding  intermediate  values  of  the 
properties  of  the  solutions  can  be  produced  in  this  way.  All  of 
these  facts  are  contained  in  the  statement  just  made,  that  the 


104  FUNDAMENTAL  PRINCIPLES  OF  CHEMISTRY 

properties  of  solutions  are  continuous  functions  of  their  composi- 
tion, and  this  is  a  general  property  of  solutions  even  in  those 
cases  where  the  properties  of  the  solution  can  no  longer  be 
calculated  from  those  of  its  constituents  as  they  can  in  the  case 
of  gases. 

84.  SEPARATION  OF  A  GAS  SOLUTION  INTO  ITS  CONSTITUENTS. 
—  The  formation  of  a  gas  solution  from  various  gases  and  the 
homogeneous  distribution  of  the  constituents  in  any  given  space 
is  a  process  which  takes  place  of  its  own  accord.  We  must  there- 
fore conclude  that  a  voluntary  separation  of  such  a  solution  into 
the  gases  which  make  it  up  (into  its  constituents)  does  not  take 
place.  As  a  matter  of  fact  we  know  of  no  process  which  takes 
place  of  its  own  accord,  that  is,  without  the  expenditure  of  external 
work,  which  also  takes  place  of  its  own  accord  in  the  opposite 
direction.  In  order  to  produce  the  constituents  from  the  solution 
work  is,  in  general,  necessary,  and  it  is  also  necessary  to  find  a 
way  in  which  such  separation  can  be  carried  out. 

The  condition  to  be  fulfilled  is  evidently  the  following :  we  must 
apply  to  the  solution  some  cause  of  motion  which  will  give  to  the 
various  constituents  of  the  gas  different  kinds  of  motion,  different 
velocities,  for  example.  By  making  use  of  differences  of  this  sort 
it  is  possible  to  cause  the  various  constituents  to  collect  in  different 
vessels.  There  are  not  very  many  processes  which  are  applicable 
in  this  way.  The  most  evident  effects  are  produced  when  gases 
pass  through  porous  solid  partitions.  When  various  gases  under 
the  same  conditions  of  temperature  and  pressure  are  forced 
through  a  partition  of  baked  clay,  they  pass  through  at  different 
rates.  If  we  have  to  deal  with  two  gases,  one  of  which  transfuses 
rapidly  and  the  other  slowly,  then  the  gas  which  passes  most 
rapidly  will  leave  the  solution  first,  and  the  one  which  transfuses 
more  slowly  will  remain  behind. 

Various  diaphragms  act  differently  in  this  respect,  but  the  order 
in  which  gases  transfuse  is  usually  the  same.  An  ideal  limiting 
case  could  be  obtained  if  we  had  a  diaphragm  which  permitted 


SOLUTIONS  105 

only  one  gas  to  pass  and  held  back  the  other  completely.  As  a 
matter  of  fact  there  is  no  diaphragm  which  acts  in  this  way,  but  an 
approximation  to  this  condition  can  be  obtained.  We  will  first 
of  all  investigate  the  ideal  limiting  case,  and  then  determine  what 
deviations  are  produced  by  the  imperfection  of  the  experimental 
method. 

85.  SEMI-PERMEABLE  DIAPHRAGMS.  —  Suppose  that  we  have 
prepared  a  solution  of  gases  A  and  B,  and  that  this  solution  is 
placed  in  a  vessel,  one  wall  of  which  permits  only  A  to  pass  and 
not  B.    Such  a  wall  is  said  to  be  semi-permeable.    A  will  leave  the 
solution  and  pass  through  this  wall,  and  if  we  arrange  to  remove 
A  from  the  other  side  of  the  wall  as  fast  as  it  passes  through,  the 
process  will  only  end  when  B  remains  alone  in  the  vessel  and  A 
has  all  passed  out. 

It  should  be  kept  in  mind  that  this  result  can  only  be  obtained 
when  A  is  taken  away  from  the  other  side  of  the  diaphragm.  If 
this  condition  is  not  fulfilled  A  will  only  pass  through  the  wall  until 
the  partial  pressure  of  A,  without  and  within,  has  become  the  same. 
At  that  point  the  cause  which  forced  A  through  the  wall  is  no 
longer  present.  It  is  in  taking  away  A  from  the  outside  of  the  wall 
that  the  work  must  be  expended  which  was  spoken  of  above. 

86.  SEPARATION  STEP  BY  STEP.  —  If  an  actual  diaphragm  is 
used  in  place  of  this  ideal  one,  it  will  exhibit  differences  in  porosity ; 
but  these  differences  will  not  be  absolute,  and  a  process  similar  to 
the  one  just  described  will  not  lead  to  a  complete  separation  of  A 
and  B.    More  A  than  B  will  pass  through  the  wall,  and  the  solu- 
tion will  thus  be  separated  into  two  parts,  of  which  one  contains 
more  of  A  and  the  other  more  of  B.    If  each  of  these  parts  is  now 
treated  separately  in  the  same  way,  the  first  quarter  will  be  still 
richer  in  A  and  the  last  quarter  still  richer  in  5.    The  two  inter- 
mediate portions  will  be  about  alike,  and  they  will  be  almost  like  the 
original  solution.    These  two  intermediate  portions  are  then  to  be 
combined  and  separated  again  by  transfusion  into  two  parts,  each  of 
which  can  be  broken  up  into  a  fraction  rich  in  A,  another  rich  in 


106 


FUNDAMENTAL   PRINCIPLES   OF  CHEMISTRY 


Bj  and  two  intermediate  portions.  The  end  fractions,  resulting 
from  the  most  complete  separation  of  the  two  gases,  can  then  be 
further  treated,  and  the  process  continued  until  the  separation  has 
become  practically  complete. 

The  following  diagram,  which  shows  the  practical  results  of  such 
a  separation,  illustrates  the  facts  just  described  more  completely 


FIG.  4. 


and  more  systematically  than  any  description.  The  separation  is 
begun  by  collecting  TV  of  the  total  amount  of  the  solution  after  it 
has  passed  through  the  diaphragm.  The  velocity  corresponding  to 
the  passage  of  each  tenth  is  plotted  vertically  on  a  horizontal  line 
divided  into  10  parts,  and  the  result  of  the  first  separation  will  give 
a  nearly  continuous  line,  somewhat  like  1  in  Fig.  4.  Each  tenth 


SOLUTIONS  107 

is  now  treated  separately  and  divided  into  two  parts,  each  of  which 
is  separately  collected.  The  first  half  of  the  first  tenth  will  pass 
through  at  nearly  the  highest  velocity  and  the  second  half  will  pass 
through  more  slowly.  The  second  tenth  is  separated  in  the  same 
way  into  two  halves,  the  first  of  which  will  be  very  nearly  like  the 
second  half  of  the  first  tenth,  while  the  second  half  will  pass  through 
more  slowly.  The  second  half  of  the  first  tenth  is  combined  with 
the  first  half  of  the  second  tenth.  The  third  tenth  is  then  separated 
into  two  halves  and  the  neighbouring  halves  combined  in  the  same 
way.  By  carrying  this  process  through  to  the  last  tenth  fractions 
will  be  obtained  which  can  be  represented  by  Fig.  5  b,  where  a 


FIG.  5. 

represents  the  first  separation.  The  double  line  indicates  the  frac- 
tions separated,  the  single  line  the  halves  which  are  afterwards 
mixed  together.  The  next  thing  is  to  separate  the  tenths  into 
halves  again  and  combine  the  neighbouring  halves  as  before. 
This  gives  the  distribution  illustrated  by  c.  Now  the  extreme 
twentieths  of  b  and  c,  which  are  most  nearly  alike,  are  combined 
as  indicated  by  the  parenthesis  signs.  This  gives  10  parts  again, 
and  with  these  the  entire  operation  of  separation  is  to  be  repeated. 
The  result  of  such  a  series  of  separations  is  shown  by  the  lines  2,  3, 
4,  and  5  of  Fig.  4,  and  the  process  is  continued  until  in  place  of 
the  line  running  almost  continuously  between  the  two  end  values, 
represented  by  1  of  Fig.  4,  a  line  like  6  of  Fig.  4  is  produced,  con- 
sisting almost  entirely  of  two  horizontal  parts. 

Theoretically  an  infinite  number  of  operations  would  be  neces- 


108  FUNDAMENTAL  PRINCIPLES  OF  CHEMISTRY 

sary  to  produce  a  complete  separation,  but  all  of  our  methods  of 
measurement  of  properties  are  finite  in  their  accuracy,  and  a  prac- 
tically complete  separation  results  from  a  finite  number  of  opera- 
tions. The  result  in  this  case  will  be  two  different  gases  each  of 
which  passes  through  the  diaphragm  with  a  definite  constant 
velocity,  so  that  during  the  entire  process  the  properties,  both  of 
the  fraction  which  passes  through  and  the  fraction  which  remains 
behind,  are  unchanged.  It  is  in  this  that  these  pure  gases  differ 
from  the  original  solution,  and  from  the  entire  set  of  solutions  pro- 
duced during  the  separation.  The  solution  changed  during  its 
passage  through  the  diaphragm ;  the  fraction  which  diffused  most 
rapidly  went  through  first  and  was  collected  outside;  the  fraction 
which  diffused  most  slowly  accumulated  in  the  residue. 

87.  ANALOGY  WITH  CHANGE  OF  STATE.  —  This  case  is  evidently 
analogous  to  the  one  described  in  Sec.  48,  where  we  discussed  the 
difference  between  a  pure  substance  and  a  solution.  In  that  case, 
however,  the  change  was  into  another  state,  and  a  mechanical  sep- 
aration was  therefore  possible,  while  in  the  case  of  a  gas  solution 
separation  has  been  achieved  by  difference  in  permeability  of  the 
diaphragm  for  the  gases.  The  similarity  is  most  evident  in  the 
case  of  the  ideal  diaphragm  which  permits  separation  to  be  car- 
ried out  in  a  single  operation,  just  as  when  a  change  of  state  has 
been  produced.  In  both  of  these  cases  a  pure  substance  is  char- 
acterized by  the  fact  that  the  residue  does  not  change  its  properties 
by  a  partial  transformation  into  another  region,  and  that  it  passes 
into  this  other  region  under  constant  conditions.  A  solution 
changes  its  properties  continuously,  and  therefore  passes  into  the 
other  region  under  continuously  changing  conditions.  Experience 
has  shown  that  when  such  a  separation  has  been  carried  out  by 
means  of  any  particular  diaphragm,  the  pure  substances  produced 
in  this  way  will  behave  like  pure  substances  with  respect  to  any 
other  diaphragm,  that  is,  they  will  pass  through  under  constant 
conditions.  The  definition  of  a  pure  substance  is  therefore  a  gen- 
eral one  and  quite  independent  of  the  special  diaphragm  used. 


SOLUTIONS  109 

And  in  the  same  way  substances  which  have  been  produced  and 
defined  as  pure  substances  by  their  behaviour  toward  permeable 
diaphragms  also  act  like  pure  substances  when  they  are  tested  by 
being  subjected  to  a  change  of  state.  The  definition  is  therefore  a 
perfectly  general  one. 

88.  PURE  SUBSTANCES.  —  Looked  at  in  this  way,  pure  sub- 
stances may  be  considered  as  limiting  cases  of  solutions.  When 
all  solutions  are  arranged  in  continuous  series  according  to  their 
properties,  so  that  every  solution  differs  from  its  neighbours  by 
only  an  indefinitely  small  amount,  the  pure  substances  form  the 
end  members  of  such  series.  Solutions  always  show  themselves 
to  be  more  or  less  variable  during  a  transformation  into  another 
state  and  during  their  passage  through  a  separating  diaphragm. 
When  these  variations  become  smaller  and  smaller  until  they 
finally  disappear,  then  a  pure  substance  has  taken  the  place  of 
a  solution.  It  is  because  they  have  their  place  at  the  ends  of  such 
continuous  series  that  pure  or  constant  substances  are  especially 
adapted  to  serve  as  the  starting  point  for  the  description  of  the 
properties  or  the  composition  of  solutions.  An  unlimited  number 
of  solutions  can  be  made  up  from  two  pure  substances,  and  the 
properties  of  these  solutions  can  vary  in  an  unlimited  number  of 
steps  between  the  values  for  the  properties  of  the  pure  substances. 
The  properties  of  the  solutions  can  all  be  expressed  by  the  prop- 
erties of  the  pure  substances.  Everything  which  needs  to  be  said 
about  a  gas  solution  has  been  expressed  when  the  properties  of  the 
pure  substances  and  the  relation  in  which  they  are  present  in  the 
solution  are  known.  This  explains  the  scientific  importance  of  a 
knowledge  of  the  properties  of  pure  substances,  and  this  knowl- 
edge was  recognized  as  the  main  object  of  chemistry  at  the  very 
beginning  of  this  book. 

So  far  we  have  assumed,  for  the  sake  of  simplicity,  that 
the  solution  contains  only  two  pure  substances  and  that  it  can 
be  separated  into  only  two.  The  discussion  becomes  more  com- 
plicated, but  is  in  no  way  fundamentally  changed,  when  three 


110  FUNDAMENTAL  PRINCIPLES  OF  CHEMISTRY 

or  more  pure  substances  or  constituents  are  considered  in  place 
of  two. 

89.  SOLUTIONS  OF  LIQUIDS  IN  GASES.  —  Gas  solutions  can  also 
be  formed  when  a  gas  and  a  liquid  are  brought  together,  provided 
the  liquid  can  evaporate,  that  is,  provided  it  can  pass  over  into  the 
state  of  a  gas.  The  law  which  describes  this  case  is  just  as  simple 
as  the  general  law  of  gas  solutions. 

It  was  shown  in  Sec.  49  that  when  a  liquid  is  brought  into  a 
vessel  of  volume  greater  than  the  volume  of  the  liquid,  it  changes 
partially  or  wholly  into  vapour.  If  the  space  above  the  liquid  con- 
tains another  substance  in  the  form  of  a  gas,  our  law  says  that  the 
liquid  will  behave  exactly  as  though  the  gas  were  not  present.  It 
will  change  into  vapour  partially  or  wholly  according  to  circum- 
stances, and  the  pressure  of  this  vapour  will  appear  as  a  partial 
pressure  added  to  the  pressure  exerted  by  the  gas  already 
present. 

Just  as  in  the  case  of  gases  (Sec.  79),  this  law  describes  only 
an  end  condition,  and,  as  in  that  case  also,  this  final  condition  re- 
quires a  longer  time  for  its  establishment  when  a  gas  is  present  in 
the  space  above  the  liquid  than  when  this  space  is  empty. 

Let  us  first  examine  the  case  where  the  volume  is  so  great  that 
the  liquid  changes  wholly  into  vapour  at  the  existing  temperature. 
If  the  space  is  empty,  the  vapour  so  produced  will  exert  a  definite 

pressure  which  is  given  by  the  equation  ^  =  r.  If  a  gas  is  al- 
ready present  in  the  space  at  a  pressure  P,  after  vaporization  is 
complete,  the  total  pressure  of  the  gas  solution  will  be  P+p. 

If  the  volume  is  so  small  that  only  a  part  of  the  liquid  can  evapo- 
rate, so  much  of  it  will  pass  into  the  vacant  space  that  a  definite 
density  and  a  definite  pressure,  corresponding  to  the  vapour  pres- 
sure p  of  the  liquid  at  the  existing  temperature,  result.  If  a  gas 
at  pressure  P  is  present  in  the  same  space,  exactly  the  same  amount 
of  the  liquid  will  evaporate,  and  the  total  pressure  of  the  gas  solu- 
tion so  produced  will  be  P+p. 


SOLUTIONS  HI 

If  we  are  dealing  with  a  volatile  solid  body  instead  of  a  volatile 
liquid  the  conditions  are  exactly  the  same. 

These  laws  were  also  discovered  by  Dalton,  and  he  derived  them 
as  consequences  of  his  fundamental  principle  that  various  gases 
in  the  same  vessel  exert  no  pressure  on  one  another.  What  Dalton 
really  meant  is  best  expressed  by  saying  that  when  several  gases 
exist  in  the  same  vessel  each  of  them  has  the  same  effect  on  the 
properties  of  the  resulting  solution  as  though  it  alone  were  present. 

90.  SATURATION.  —  In  analogy  with  other  cases  which  will 
be  considered  later  we  will  call  the  condition  in  which  liquid  and 
gas  solution  exist  together  one  of  saturation  of  the  gas  with  liquid. 
This  use  of  the  term  is  not  a  customary  one,  but  it  is  perfectly  cor- 
rect, and  it  is  usual  to  say  that  the  gas  is  saturated  with  the  vapour 
of  the  liquid.  The  condition  of  saturation  is  characterized  by  the 
fact  that  the  composition  of  the  solution  becomes  independent  of 
the  proportions  of  the  substances  which  form  it.  If  more  liquid 
is  added  it  remains  liquid  in  contact  with  the  gas  solution,  and 
the  composition  of  the  latter  is  not  changed  by  any  such  addition 
of  liquid,  provided  temperature  and  pressure  are  kept  constant. 
The  only  thing  which  has  been  changed  in  this  case  is  the  relative 
amounts  of  the  two  phases  which  are  present.  In  our  discussion 
of  the  equilibrium  between  the  various  states  of  a  substance  we 
learned  the  principle  that  the  absolute  and  relative  amounts  of 
the  phases  which  are  present  have  no  influence  whatever  on  the 
equilibrium.  We  have  now  a  further  example  of  this  principle, 
which  is,  in  fact,  a  very  general  one. 

It  is  not  difficult  to  show  the  necessity  of  this  principle.  A  mutual 
influence  of  the  two  phases  can  appear  only  at  their  surface  of  con- 
tact. Suppose  that  equilibrium  already  exists  at  this  surface  be- 
tween the  neighbouring  portions  of  the  two  phases.  Equilibrium 
already  exists  between  these  parts  of  each  phase  and  those  parts 
of  the  same  phase  which  are  further  removed  from  the  boundary 
surface,  for  all  properties  are  the  same  in  every  part  of  the  phase. 
The  region  occupied  by  any  phase  can  therefore  be  increased  at 


112  FUNDAMENTAL  PRINCIPLES  OF  CHEMISTRY 

will  without  any  change  in  the  condition  of  equilibrium,  and 
therefore  the  amount  of  any  phase  has  no  effect  on  the  existence 
of  equilibrium.  In  the  case  in  question  the  addition  of  liquid  only 
means  that  the  amount  of  the  liquid  phase  is  increased ;  the  com- 
position of  the  gas  solution  remains  quite  unchanged  by  any  such 
addition. 

91.  THE  INFLUENCE  OF  PRESSURE.  —  It  is  not  difficult  to  see 
what  influence  pressure  has  on  this  equilibrium.  If  the  pressure 
is  increased,  the  density  of  the  gas  will  increase  proportionately. 
If  an  amount  of  the  volatile  liquid  which  is  insufficient  to  cause 
saturation  is  allowed  to  enter  the  space  occupied  by  the  denser 
gas,  then  the  conditions  are  the  same  as  before.  The  liquid  evapo- 
rates and  adds  its  partial  pressure  to  that  of  the  gas.  When  this 
partial  pressure  has  reached  the  vapour  pressure  of  the  liquid 
no  more  of  the  latter  will  evaporate,  and  we  will  again  have  a 
saturated  gas  solution.  This  will  have  a  different  composition 
from  the  former  one,  for  while  the  partial  pressure  of  the  vapour 
has  remained  the  same,*  that  of  the  gas  was  greater  from  the 
beginning.  In  the  resulting  saturated  solution  there  is  therefore 
a  larger  proportion  of  the  gas,  corresponding  to  the  higher 
pressure. 

It  may  be  said  that  in  general  the  composition  of  the  saturated 
gas  solution  will  vary  in  such  a  way  that  the  ratio  of  gas  to  vapour 
varies  proportionately  with  the  partial  pressure  of  the  gas. 

It  is-  evident  from  this  that  saturation  does  not  depend  only  on 
the  nature  of  the  substances  which  take  part,  although  this  has 
been  assumed  very  often  as  a  deduction  from  the  well-known  case 
of  a  solution  of  solids  in  liquids.  Saturation  is  a  case  of  equili- 
brium, varying  with  the  nature  of  the  phases  which  take  part,  and 
in  which  the  same  substances  may  appear  in  very  different  rela- 
tions under  different  conditions. 

*  This  statement  is  not  entirely  correct,  for  the  vapour  pressure  of  a  volatile 
liquid  is  not  entirely  independent  of  the  pressure  under  which  the  liquid  exists. 
The  effect  of  pressure  is,  however,  small,  and  can  be  neglected  here  for  the 
sake  of  simplicity. 


SOLUTIONS  113 

02.  THE  EFFECT  OF  TEMPERATURE.  —  The  saturation  equili- 
brium in  question  is  dependent  upon  temperature  as  Well  as  upon 
pressure.  At  constant  volume  it  is  evident  that  the  proportion  of 
vapour  in  the  gas  solution  must  increase  as  the  vapour  pressure 
of  the  liquid  increases.  As  the  temperature  rises,  more  and  more 
of  the  volatile  liquid  will  dissolve  in  the  gas,  and  at  the  critical 
point  solution  in  all  proportions  will  be  the  result.  The  nature  of 
the  gas  has  no  particular  influence,  and  the  effect  of  temperature 
is  therefore  the  same  whatever  gas  is  used.  The  effect  of  tempera- 
ture is  also  independent  of  pressure,  which  means,  as  we  have 
shown,  that  it  is  independent  of  the  density  of  the  gas.  The  varia- 
tion of  solubility  with  the  temperature  is  therefore  a  function  only 
of  the  properties  of  the  liquid  which  is  dissolving  in  the  gas.  This 
is  one  conclusion  from  the  principle  that  a  gas  in  any  given  space 
behaves  in  exactly  the  same  way  whether  the  space  is  filled  with 
other  gases  or  not. 

93.  THE  PHASE  RULE.  —  If  we  endeavour  to  bring  this  case 
under  the  phase  rule  of  Sec.  61  it  will  be  found  necessary  to  ex- 
tend this  rule  somewhat.  We  have  here  two  phases,  a  liquid  one 
and  a  gaseous  one,  and  nevertheless  we  have  two  degrees  of  free- 
dom, for  we  can  vary  the  temperature  without  fixing  the  pressure. 
Pressure  is  therefore  free,  and  the  sum  of  phases  and  degrees  of 
freedom  is  four  in  place  of  three  as  in  former  cases.  Another 
difference  goes  hand  in  hand  with  this  one.  In  the  earlier  cases 
of  transformation  from  state  to  state  each  phase  could  be  trlans- 
formed  completely  into  each  other  phase  (liquid  water  into  water 
vapour  or  ice,  etc.).  This  is  no  longer  the  case  here.  The  gas 
phase  consists  of  a  solution  of  gas  and  vapour  in  proportions 
changing  as  temperature  and  pressure  are  changed.  The  liquid 
phase  is  the  liquid  which  has  dissolved  a  small  and  variable  amount 
of  the  gas.  And  so  while  in  the  earlier  case  the  condition  and  the 
properties  of  a  phase  were  completely  determined  by  two  varia- 
bles, pressure  and  temperature,  in  the  case  under  consideration 
this  no  longer  holds  true.  The  composition  of  a  phase  can  be  a 
8 


114  FUNDAMENTAL   PRINCIPLES   OF  CHEMISTRY 

variable  one.  If  two  constituents  are  involved  a  single  statement 
determines  the  composition  of  the  phase,  and  that  is  the  propor- 
tion by  weight  in  which  the  two  constituents  are  present.  If  three 
constituents  are  involved  two  such  statements  are  necessary.  If, 
for  example,  A,  B,  and  C  are  the  three  constituents,  the  composi- 

A         ."A-, 

tion  is  given  when   two   proportions  ~  and  -~,  for  example,  are 

Jo 

D 

known.     The  third  proportion    —  can  be  obtained  from  these  by 

C 

division.  If  then  B  constituents  are  involved,  B  —  l  statements 
are  necessary  to  fix  the  composition  of  a  phase. 

Beside  the  freedoms  corresponding  to  pressure  and  tempera- 
ture, we  have  therefore  to  consider  others  which  depend  upon  the 
composition  of  a  variable  phase.  Solutions  are  phases  of  variable 
composition.  Depending  on  whether  the  composition  can  be 

expressed  -by  1,  2, B  —  l  arbitrary  variables,  we  speak  of 

2,  3 B  constituents.  Beside  the  two  freedoms  corresponding 

to  pressure  and  temperature,  we  therefore  have  for  B  constituents 
B  —  1  further  degrees  of  freedom. 

These  degrees  of  freedom  can  either  be  controlled  directly,  or 
by  setting  the  condition  that  several  phases  shall  exist  together  in 
equilibrium.  If  we  are  controlling  them  directly,  we  are  dealing 
with  a  single  phase,  and  we  have  therefore  2+5  —  1=5  +  1  de- 
grees of  freedom  where  B  is  the  number  of  constituents.  If 
two  phases  are  to  exist  together,  only  B  degrees  of  freedom  will  be 
left,  and  if  P  phases  are  to  exist  together,  this  means  an  addition 
of  P  —  2  phases,  and  the  number  of  degrees  of  freedom  is  dimin- 
ished by  P-2.  This  gives  B-  (P-2)=5-P  +  2  degrees  of 
freedom.  If  F  is  the  number  of  degrees  of  freedom  the  general 
law  says  F=5-P  +  2orF+P=5+2.  In  this  latter  form  the 
phase  rule  is  perhaps  easiest  to  remember.  The  sum  of  degrees 
of  freedom  and  phases  is  equal  to  the  number  of  components 
plus  2. 

It  is  easy  to  see  that  the  phase  rule  can  be  applied  to  the  simpler 


SOLUTIONS  115 

cases  which  we  have  already  studied,  in  which  only  one  compo- 
nent was  present.  The  sum  of  phases  and  degrees  of  freedom 
must  in  this  case  be  3,  and  we  found  this  to  be  the  case  in  Sec.  61. 
The  rule  is  also  applicable  to  the  case  which  led  to  the  present 
discussion.  We  had  two  components  and  two  phases;  the  sum 
is  4,  and  two  degrees  of  freedom  remain.  And  in  fact  in  a  system 
consisting  of  liquid  and  gas  both  temperature  and  pressure  can 
be  changed  freely  and  independently,  as  we  have  already  seen. 

94.  COMPONENTS.  —  The  idea  of  a  component  was  necessary 
in  the  expression  of  the  phase  rule,  and  it  is  therefore  advisable 
to  find  out  exactly  what  is  understood  by  this  term.  Where  we 
assumed  only  one  component,  the  case  was  characterized  by  the 
fact  that  every  phase  which  could  be  produced  from  another 
phase  by  a  change  of  pressure  and  temperature  could  be  produced 
from  this  other  phase  alone.  No  other  phase  was  necessary  for 
its  production,  and  no  other  phase  remained  behind  after  the 
transformation;  each  phase  could  be  transformed  completely  into 
each  other  phase.  When  this  condition  is  fulfilled,  and  only  then, 
we  speak  of  one  component.  We  can  express  this  by  saying  that 
we  are  dealing  with  one  component,  when  one  single  phase  is 
sufficient  for  the  production  of  any  phase. 

It  is  evidently  not  necessary  that  these  phases  should  be  in 
equilibrium.  If  we  wish  to  make  ice  we  can  use  water  vapour  at 
any  pressure  whatever,  provided  the  temperature  is  lowered  to 
a  corresponding  point.  The  phase  from  which  the  other  phase  is 
produced  can  therefore  be  chosen  anywhere  in  the  whole  region 
of  pressures  and  temperatures  within  which  the  system  is  to  be 
investigated,  provided,  of  course,  that  this  phase  can  exist  under 
the  conditions  chosen. 

If  one  phase  is  not  sufficient  to  produce  any  other  phase  in  the 
system  in  question  we  speak  of  several  components.  In  every 
such  case  we  are  dealing  with  a  solution,  and  solutions  may  there- 
fore be  defined  as  homogeneous  substances  produced  by  com- 
bining several  components  in  arbitrary  proportions.  We  shall 


116  FUNDAMENTAL  PRINCIPLES  OF  CHEMISTRY 

consider  pure  substances  as  components  in  this  sense,  that  is,  as 
substances  from  which  solutions  can  be  made,  for  it  is  a  general 
fact  of  experience  that  any  solution  can  be  prepared  from  pure 
substances.  It  is,  however,  not  necessary  that  this  should  be  the 
case.  Solutions  might  be  used  in  the  preparation  of  new  solutions, 
but  this  process  is  more  limited  in  its  application.  If  we  have, 
for  example,  two  solutions  containing  the  same  components  but 
in  different  proportions,  it  is  possible  to  prepare  by  proper  mixing 
all  these  solutions  whose  composition  with  respect  to  one  com- 
ponent lies  between  the  composition  of  the  two  solutions,  but  not 
those  containing  a  larger  proportion  of  one  or  other  of  the  com- 
ponents. It  is  in  every  way  most  useful  to  consider  the  pure  sub- 
stances into  which  the  individual  phases  can  be  analyzed  as  the 
components  of  the  system.  This  is  not,  however,  strictly  necessary, 
for  if  we  chose  those  among  the  possible  phases  of  a  system  which 
lie  at  the  extreme  limits,  as  far  as  composition  is  concerned,  it  is 
evident  that  even  though  they  are  not  pure  substances  it  will  be 
possible  to  make  up  all  the  other  phases  from  them. 

The  whole  possible  set  of  systems  have  been  subdivided  into 
those  in  which  two  phases  are  sufficient  for  the  formation  of  all 
the  other  phases,  and  others  in  which  three,  four,  five,  etc.,  phases 
are  necessary.  Based  on  this,  we  speak  of  two,  three,  or  more 
components  of  a  system,  for  since  the  relative  amounts  of  these 
which  are  necessary  to  produce  all  the  other  phases  can  be  ar- 
bitrarily varied  within  certain  limits,  they  provide  us  with  a  cor- 
responding number  of  degrees  of  freedom  as  far  as  composition 
is  concerned.  The  number  of  degrees  of  freedom  so  produced  is 
always  one  less  than  the  number  of  phases  required. 

Considered  from  this  point  of  view,  the  pure  substances  are 
limiting  cases  of  solutions,  and  they  are  especially  characterized 
by  the  fact  that  all  possible  solutions  can  be  prepared  from  them, 
while  this  is  not  the  case  with  solutions  of  fixed  and  finite  com- 
position. It  would  be  possible,  if  we  could  have  negative  amounts 
of  a  substance,  to  represent  all  possible  cases  as  resultant  from 


SOLUTIONS  117 

two  (or  three  or  more)  solutions.  This  supposition  does  not, 
however,  correspond  to  any  known  physical  possibility,  and  there- 
fore pure  substances  are  of  importance  in  defining  and  expressing 
the  properties  of  solutions. 

95.  COMPOSITION.  —  The  fact  that  in  a  system  containing  only 
one  component  any  phase  can  be  formed  from  any  other  without 
residue  is  often  expressed  by  saying  that  each  phase  has  the  same 
composition  as  every  other  phase.  This  expression  has  evidently 
been  borrowed  from  the  more  complicated  cases,  for  certainly  in 
this  case  no  phase  is  "  composed  "  of  any  other  substances,  and 
all  are  equally  simple.  Such  a  system  is  said  to  be  of  the  first 
order.  Second  order  systems  are  those  where  two  phases  are  neces- 
sary for  the  formation  of  a  third,  and  the  nomenclature  is  similar 
for  systems  of  higher  order. 

It  is  evident  that  our  whole  discussion  is  without  meaning  unless 
more  than  one  phase  is  present.  As  long  as  only  one  is  present,  it 
is  without  meaning  to  ask  the  question  whether  it  can  be  produced 
from  other  phases  not  present  and  unknown.  It  is  only  when  a 
second  phase  has  appeared  as  a  result  of  a  change  in  pressure  or 
temperature  that  the  question  whether  or  not  the  second  phase 
has  the  same  composition  as  the  first  can  be  asked  and  answered. 
The  question  is  identical  with  asking  whether  the  change  from  one 
to  the  other  goes  on  under  constant  conditions  or  not.  If  it 
does,  the  properties  of  the  residuum  of  either  phase  must  always  be 
the  same,  whatever  the  amount  of  this  phase  transformed  or  re- 
maining. Since  the  properties  of  solutions  vary  continuously  with 
their  composition,  a  phase  which  changes  its  properties  continu- 
ously during  transformation  into  another  phase  must  also  be  a 
solution,  for  its  composition  must  have  changed  if  its  properties 
did.  A  decision  in  the  reverse  direction  is  not  so  simple  a  matter. 
It  is  quite  imaginable  that  a  solution  passing  from  one  phase  to 
another  changes  into  a  solution  of  the  same  composition,  and 
then  the  transformation  will  of  course  take  place  under  constant 
conditions  of  temperature  and  pressure.  But  under  other  con- 


118  FUNDAMENTAL  PRINCIPLES   OF   CHEMISTRY 

ditions,  at  other  temperatures  and  pressures,  or  in  the  formation  of 
a  phase  in  some  other  state,  such  a  solution  will,  in  general,  change 
into  a  solution  having  another  composition,  and  then  the  trans- 
formation will  no  longer  take  place  under  constant  conditions. 
For  when  the  new  phase  has  a  different  composition  from  the  old 
one,  there  must  be  a  change  in  the  composition  of  the  residue  dur- 
ing the  transformation,  and  this  would  bring  with  it  a  change  in 
the  conditions  of  transformation  —  in  the  boiling  or  freezing  point, 
for  example. 

It  may  be  concluded  that  our  former  definition  of  a  solution,  as 
a  homogeneous  substance  which  freezes  and  boils  under  continu- 
ously varying  conditions,  agrees  well  with  the  other  definition  that 
solutions  are  homogeneous  phases  which  can  be  formed  from  com- 
ponents in  any  arbitrary  proportions  whatever. 

96.  LIQUID  SOLUTIONS.  —  Gaseous  solutions  exhibit  the  same 
general  properties  as  pure  gases,  and  liquid  solutions  are  so  similar 
to  pure  liquids  that  it  is  usually  quite  impossible  to  tell  whether  or 
not  a  liquid  is  a  solution  by  any  indirect  process  of  investigation. 
It  is  only  by  exposing  it  to  an  action  which  causes  it  to  go  over  in 
part  into  another  condition  (by  freezing  or  boiling,  for  example) 
that  the  characteristics  of  a  solution  appear.  Freezing  or  boiling 
does  not  take  place  at  constant  temperature  and  pressure,  and  a 
condition  of  equilibrium  dependent  on  the  proportion  of  the  two 
phases  is  set  up. 

It  makes  no  difference  whatever  how  a  solution  is  produced  from 
its  constituents  as  far  as  its  properties  are  concerned,  and  this 
statement  applies  equally  to  all  kinds  of  solutions.  If  a  solution 
consists  of  the  two  substances  A  and  B,  it  is  the  same  whether  the 
substance  A  is  added  in  the  liquid,  solid,  or  gaseous  state,  provided, 
of  course,  the  proportions  by  weight  are  the  same  and  tem- 
perature and  pressure  agree  in  each  case.  The  states  correspond- 
ing to  the  various  substances  involved  are  only  important  when 
the  solution  is  to  be  investigated  in  equilibrium  with  other  phases, 
that  is,  when  the  substances  involved  are  actually  present  in  their 


SOLUTIONS  119 

original  states  in  contact  with  the  solution.  Two  wholly  different 
groups  of  properties  are  therefore  to  be  distinguished  in  the  study 
of  solutions:  those  which  appertain  to  the  solution  alone,  and 
those  which  express  equilibrium  between  the  solution  and  other 
phases.  In  the  first  case  only  one  single  phase,  the  solution  itself, 
is  present  or  needs  consideration.  In  the  other  case  at  least  two 
phases  are  to  be  considered.  This  same  difference  was  found 
between  systems  of  pure  substances  involving  one  and  more 
than  one  phase.  In  the  first  case  we  are  dealing  with  specific 
properties,  and  in  any  other  case  we  are  dealing  with  an 
equilibrium. 

We  have  already  considered  the  general  properties  of  liquids, 
and  a  similar  set  of  properties  belong  to  liquid  solutions.  The 
coefficients  of  compressibility  and  of  expansion  are  small  and  vary 
from  case  to  case.  Each  solution  as  well  as  each  pure  substance 
has  its  own  special  values  for  these  and  all  other  properties.  The 
difference  is  found  in  the  fact  that  while  among  pure  substances 
properties  differ  by  jumps,  among  solutions  it  is  usually  possible 
to  produce  one  which  differs  in  properties  from  another  by  as 
little  as  we  choose.  The  properties  of  liquid  solutions  are  continu- 
ous functions  of  their  composition,  calculated  in  terms  of  the  pure 
substances  of  which  they  are  composed.  They  are  not  like  gas 
solutions,  however.  Their  properties  can  not  be  calculated  by  the 
simple  rule  of  mixtures  from  those  of  their  constituents.  It  is 
usually  true  that  the  real  value  of  any  property  is  found  on  care- 
ful measurement  to  differ  measurably  from  the  value  calculated 
by  this  rule.  The  deviation  may  be  either  positive  or  negative, 
that  is,  the  real  value  can  be  either  smaller  or  larger  than  the  cal- 
culated one.  The  form  in  which  the  property  is  expressed  often 
determines  the  direction  of  the  variation.  The  volume  occupied 
by  a  solution  is,  in  general,  different  from  the  volume  occupied  by 
the  constituents  before  they  were  mixed.  If  it  is  smaller,  the  devi- 
ation would  be  called  a  negative  one.  But  this  means,  of  course, 
that  the  density  of  the  solution  is  greater  than  that  calculated  by 


120  FUNDAMENTAL  PRINCIPLES  OF  CHEMISTRY 

the  rule  of  mixtures,  and  if  this  is  taken  as  the  form  in  which  the 
property  is  expressed,  the  deviation  will  be  a  positive  one. 

Such  deviations  are,  in  general,  smaller  as  the  solution  is  more 
dilute;  that  is,  as  one  or  other  of  the  constituents  is  present  in  great 
excess.  No  deviation  is,  of  course,  possible  in  the  pure  substance, 
which  is  at  the  limit  of  the  series  of  solutions.  The  amount  of  the 
deviation  must  therefore  be  small  in  dilute  solutions,  approaching 
zero  with  dilution.  The  conclusion  is  based  on  the  general  law  that 
all  the  properties  of  solutions  are  continuous  functions  of  their  com- 
position. If  then  the  composition  is  varied  by  an  infinitesimal 
amount,  properties  must  vary  by  an  equally  small  amount. 

Solvent  and  Solute  are  often  distinguished  in  speaking  of  solu- 
tions. These  are  arbitrary  terms,  and  we  understand  by  solvent 
that  constituent  which  makes  up  the  larger  portion  of  the  solu- 
tion. If  we  consider  a  solution  made  of  equal  parts  of  its  con- 
stituents this  could  not  be  applied,  and  if  the  composition  were 
changed  so  that  it  passed  through  this  point  (50  per  cent  of  each 
constituent),  then  the  two  constituents  would  have  to  change 
names  suddenly.  The  solvent  would  become  the  solute,  and  vice 
versa.  The  properties  would,  of  course,  vary  only  slightly  and 
continuously.  We  shall  be  careful  to  apply  the  term  "  solvent " 
only  where  we  wish  to  indicate  that  one  constituent  is  in  excess 
under  the  particular  circumstances  in  question. 

97.  SOLUTIONS  OF  GASES  IN  LIQUIDS.  —  Liquid  solutions  may 
be  formed  when  either  gases,  liquids,  or  solids  are  dissolved  in  a 
liquid.  They  are  occasionally  formed  between  solids  or  gases,  but 
these  cases  are  rarer  and  will  be  considered  separately.  The  first 
case  to  be  considered  here  is  a  solution  of  a  gas  and  a  liquid. 

A  general  law  is  applicable  in  this  case,  for  all  gases  can  form 
liquid  solutions  with  all  liquids.  In  this  respect  these  liquid  solu- 
tions are  like  gaseous  ones,  but  they  do  not  agree  with  the  latter 
because  the  proportions  of  gas  and  liquid  are  not  unlimited.  Only 
a  limited  amount  of  a  gas  will  dissolve. 

If  a  very  small  amount  of  a  gas  is  brought  in  contact  with  a  given 


SOLUTIONS  121 

amount  of  a  liquid  under  given  and  constant  conditions  of  tem- 
perature and  pressure,  the  gas  disappears  as  a  phase  and  a  homo- 
geneous liquid  results.  The  properties  of  this  liquid  differ  less  and 
less  from  those  of  the  pure  liquid  used  as  the  proportion  of  gas  to 
liquid  is  made  smaller  and  smaller.  The  properties  of  the  solu- 
tions formed  from  the  two  constituents  vary  continuously  with  the 
properties  of  the  pure  liquid  as  one  limit.  In  this  respect  liquid 
solutions  are  like  gaseous  ones,  but  their  properties  cannot  be  cal- 
culated beforehand  from  those  of  the  constituents. 

If  now  we  increase  the  proportion  of  gas  little  by  little,  these 
added  amounts  will  at  first  disappear  and  the  properties  of  the  so- 
lution so  formed  will  differ  more  and  more  from  those  of  the  pure 
liquid.  Between  any  two  different  solutions  formed  of  different 
proportions  of  liquid  and  gas  any  number  of  other  solutions  can 
be  added,  made  up  of  proportions  lying  between  those  of  the  two 
end  solutions.  In  other  words,  these  solutions  make  up  a  continu- 
ous series  with  respect  to  composition  as  well  as  properties,  or  we 
can  say,  the  properties  of  solutions  are  continuous  functions  of 
their  composition. 

When  the  relative  amount  of  the  gas  has  reached  a  definite 
value  no  more  gas  will  be  dissolved  by  the  liquid,  and  the  excess  of 
gas  forms  a  separate  phase  in  contact  with  the  solution.  No 
matter  how  much  gas  is  now  added,  no  change  is  produced  in  the 
properties  of  the  solution,  and  the  gas  added  simply  collects  in  the 
gas  phase.  Such  a  solution  in  equilibrium  with  another  phase  is 
said  to  be  saturated  (Sec.  51). 

98.  THE  LAW  OF  ABSORPTION.  A  very  different  system  is  pro- 
duced when  the  volume  of  the  system  of  gas  and  liquid  is  kept  con- 
stant instead  of  the  pressure.  Imagine  a  liquid  brought  into  a 
vessel  which  is  not  wholly  filled  by  it,  and  a  small  amount  of  a  gas 
added.  A  solution  of  gas  in  liquid  will  be  produced,*  but  the  gas 

*  Generally  a  part  of  the  liquid  will  also  evaporate  and  the  gas  phase 
will  become  a  solution.  To  avoid  making  our  discussion  too  complex  at 
first  we  will  assume  that  the  liquid  has  so  small  a  vapour  pressure  that  it  may 
be  neglected. 


122  FUNDAMENTAL  PRINCIPLES  OF  CHEMISTRY 

phase  cannot  wholly  disappear  because  the  liquid  does  not  fill  the 
whole  volume  of  the  vessel.  Only  a  part  of  the  gas  will  go  into 
solution,  and  the  remainder  will  fill  the  free  space  under  reduced 
pressure.  If  now  we  add  more  gas,  a  new  distribution  between 
gas  and  solution  will  result.  Each  addition  of  gas  will  deter- 
mine an  equilibrium  between  the  two  phases,  and  we  are  to  see 
whether  it  is  possible  to  express  the  conditions  of  equilibrium  in 
a  definite  way. 

First  of  all  we  must  remember  that  an  equilibrium  of  this  kind 
is  not  affected  by  the  absolute  or  relative  amounts  of  the  two 
phases.  It  is  only  to  be  expressed  in  terms  which  are  independent 
of  these  values.  The  concentration  expresses  what  we  need,  and 
this  is  the  relation  between  amount  of  substance  and  space  which 
it  occupies.  In  the  gas  phase  it  is  equal  to  the  density.  For  the 
solution  we  could  develop  the  idea  of  a  partial  density,  analogous 
to  that  of  partial  pressure  (Sec.  81),  and  then  the  concentration 
will  be  equal  to  the  partial  density,  that  is,  to  the  amount  of  the 
dissolved  gas  divided  by  the  volume  of  the  solution  containing  it. 
The  term  "  concentration  "  is  more  usual,  and  we  shall  therefore 
use  it  as  well  as  the  partial  density. 

For  a  solution  of  a  gas  and  a  liquid  the  following  law  holds :  At 
equilibrium  the  partial  densities  of  the  gas  in  the  two  phases  are  in  a 
constant  ratio  which  is  independent  of  the  pressure.  If  the  pressure 
in  the  gas  phase  (and  the  density,  which  is  proportional  to  the 
pressure)  is  trebled,  the  partial  pressure  of  the  gas  in  the  liquid 
phase  will  also  be  trebled,  and  this  means  that  saturation  will 
occur  when  three  times  the  original  amount  of  gas  has  been  dis- 
solved. The  ratio  of  the  density  in  the  gas  phase  to  the  partial 
density  in  the  liquid  one  is  called  the  relative  solubility  of  the  gas. 
Our  law  can  be  also  expressed  as  follows :  The  relative  solubility 
of  a  gas  is  independent  of  pressure.  But  the  absolute  solubility, 
the  weight  of  gas  taken  up  by  unit  volume  of  the  liquid,  is  propor- 
tional to  the  pressure  and  therefore  to  the  density  of  the  gas. 

This  important  law  was  discovered  by  Henry  and  later  tested 


SOLUTIONS  123 

and  confirmed  by  Bunsen.  It  does  not  hold  for  all  gas  solutions, 
but  only  for  those  which  contain  a  comparatively  small  amount 
of  gas. 

99.  SOLUTIONS  OF  LIQUIDS  IN  LIQUIDS.  —  If  small  amounts  of 
one  liquid  are  added  to  another  liquid,  a  liquid  solution  generally 
results  with  properties  nearly  similar  to  those  of  the  liquid  present 
in  excess.    We  must  assume  that  every  liquid  dissolves  every  other 
one,  though  often  only  in  extremely  minute  amount.  £Since  every 
liquid  dissolves  every  gas,  and  since  every  liquid  possesses  a  cer- 
tain (often  very  small)  vapour  pressure,  we  must  conclude  that 
every  liquid  will  dissolve  the  vapour  of  every  other  liquid^  As  far 
as  the  properties  of  the  resulting  solution  are  concerned,  it  makes 
no  difference  how  it  is  prepared,  and  if  a  solution  can  be  made 
from  a  liquid  and  a  vapour,  it  can  also  be  made  from  the  liquid 
and  the  liquid  obtained  by  liquefying  the  same  vapour. 

Experience  has  confirmed  this  general  conclusion  in  those  cases 
where  we  possess  delicate  methods  of  analysis  for  the  dissolved 
liquid.  Every  increase  in  our  knowledge  of  methods  extends  the 
number  of  solvents  for  the  substance  in  question,  [and  the  conclu- 
sion is  justified  that  with  fine  enough  methods  we  could  prove  the 
solubility  of  all  liquids  in  one  anothejrj  Such  an  assumption  corre- 
sponds most  nearly  to  all  of  our  experience  so  far. 

A  conclusion  of  this  kind,  by  which  a  limited  set  of  experiences 
is  expanded  to  include  a  wider  range  of  similar  but  unexplored 
cases,  is  called  an  inductive  conclusion,  and  in  the  case  described 
it  would  be  called  an  incomplete  induction.  A  conclusion  of  this 
sort  brings  with  it  no  certainty,  but  only  a  probability,  and  the  de- 
gree of  its  probability  depends  on  the  degree  of  similarity  in  the 
two  cases  compared.  Such  conclusions  play  a  very  important 
part  in  the  natural  sciences  and  aid  greatly  in  our  advancement  in 
knowledge.  But  until  an  actual  experimental  proof  has  been 
secured  it  must  be  remembered v that  an  error  is  always  possible. 

100.  UNLIMITED  SOLUBILITY.  --If  the  amount  of  the  second 

% 

liquid  which  is  added  to  the  first  is  increased  indefinitely  two  cases 


124  FUNDAMENTAL   PRINCIPLES  OF  CHEMISTRY 

are  possible.  All  these  additions  may  be  dissolved,  and  new  homo- 
geneous solutions  with  continuously  varying  properties  may  be 
formed.  Or,  after  a  certain  relative  amount  has  been  added,  a 
further  amount  of  the  second  liquid  does  not  go  into  solution,  but 
remains  as  a  second  liquid  phase  in  contact  with  the  first.  The 
first  case  is  that  of  unlimited  solubility. 

As  more  and  more  of  the  second  liquid  is  added,  its  proportional 
amount  increases,  and  the  solution  becomes  more  anjl  more  like  the 
second  liquid.  All  possible  solutions  therefore  form  a  continuous 
series,  passing  from  the  first  liquid  to  the  second,  and  bounded  by 
these  two  liquids.  If  these  are  pure  substances,  their  solutions 
form  a  continuous  set  with  properties  varying  between  the  prop- 
erties of  these  pure  substances.  So  far  the  liquid  solutions  agree 
in  their  behaviour  with  the  gaseous  ones;  but  in  these  latter  un- 
limited solubility  is  the  rule,  while  in  the  liquids  it  is  a  special  case, 
and  not  the  most  usual  one  at  that. 

Another  important  difference  is,  that  although  the  properties  of 
liquid  solutions  form  a  continuous  series  from  those  of  one  "con- 
stituent to  those  of  the  other,  they  cannot  be  calculated  by  simple 
addition.  The  properties  of  liquid  solutions  usually  exhibit  more 
or  less  pronounced  deviation  from  those  calculated  from  the  rule 
of  mixtures,  and  these  deviations  have  so  far  not  been  found  to 
exhibit  any  general  regularities. 

If  the  composition  of  all  possible  solutions  of  two  components 
is  plotted  along  a  horizontal  line,  and  perpendiculars  are  erected 
at  each  point  expressing  the  value  of  any  property  of  the  various 
solutions,  the  ends  of  all  these  perpendiculars  will  form  a  contin- 
uous line,  and  the  two  ends  of  this  line  will  express  the  value  of 
the  property  in  question  for  the  pure  components.  For  gases  this 
line  will  be  straight,  for  in  this  case  the  properties  of  the  compo- 
nents are  not  affected  by  the  process  of  solution,  and  they  therefore 
vary  in  the  proportion  of  the  fractions  of  the  components  in  the 
solution,  all  of  which  is  expressed  by  the  straight  line.  In  liquid 
solutions  this  line  is,  as  a  rule,  not  straight,  although  there  are 


SOLUTIONS 


125 


some  cases  in  which  the  deviations  from  the  straight  line  lie 
within  the  experimental  errors. 

Such  a  line  is  always  continuous,  that  is,  it  has  nowhere  any 
sharp  corners  or  breaks.  This  fact  was  to  be  anticipated  as  the 
result  of  the  continuity  in  proportional  relation  in  which  the  com- 
ponents can  be  dissolved.  This  principle  has  often  been  doubted, 
and  it  has  been  proven  by  careful  experimental  investigation  that, 
as  a  matter  of  fact,  continuity  is  present  in  all  those  cases  which 
have  been  carefully  examined.  The  inductive  conclusion  that 
continuity  is  a  general  phenomenon  is  therefore  a  very  probable 
one. 

101.  MAXIMA  AND  MINIMA.  — A  deviation  from  a  straight  line 
can  take  place  in  such  a  way  that  the  curved  line  lies  either  above 
or  below  a  straight  one 

drawn    between    the   two  c 

end  points.  These  cases 
are  shown  in  the  curves  a 
and  6  of  Fig.  6,  and  both 
these  cases  have  been  ob- 
served. More  complicated 
lines  are  also  possible. 

With  greater  and  greater 
curvature  lines  like  c  and 
d  can  appear.  In  this  case 
the  properties  of  certain 
solutions  no  longer  lie  be- 
tween the  properties  of  the 

pure  substances  of  which  they  are  formed,  but  extend  beyond  them. 
These  curves  have  a  maximum  or  a  minimum,  and  in  such  cases 
there  always  exists  a  solution  possessing  the  same  value  of  the 
property  as  belongs  to  one  of  the  pure  components.  The  com- 
position of  this  solution  is  found  by  drawing  a  horizontal  line 
from  the  point  corresponding  to  the  component  and  finding  the 
place  where  it  cuts  the  curve.  If  the  curve  shows  a  minimum, 


FIG.  6. 


126  FUNDAMENTAL   PRINCIPLES   OF   CHEMISTRY 

this  solution  is  similar  to  the  component  possessing  the  lower 
value  of  the  property.  If  it  exhibits  a  maximum,  the  solution  is 
like  the  other  component.  All  this  is  evident  at  a  glance  from 
Fig.  6.  ' 

It  is  also  evident  that  a  maximum  or  a  minimum  will  occur 
more  easily,  that  is,  as  a  result  of  a  smaller  deviation  of  the  curve 
from  a  straight  line,  when  the  values  of  the  property  are  nearest 
alike  in  the  two  components.  If  these  values  are  the  same,  the 
two  end  points  of  the  curve  lie  at  the  same  height  above  the  base 
line,  and  any  deviation  from  a  straight  line  necessarily  leads  to 
a  maximum  or  a  minimum.  In  this  limiting  case  all  the  values 
of  the  properties  of  the  solution  lie  outside  those  of  the  components. 

The  presence  of  a  maximum  or  a  minimum  (a  singular  value 
in  general)  often  indicates  special  peculiarities  of  the  corresponding 
solution.  We  shall  have  occasion  to  examine  cases  of  this  sort 
later. 

102.  LIMITED  SOLUBILITY.  —  Let  us  now  examine  the  case 
where  two  liquids  dissolve  each  other  only  within  certain  limits. 
Starting  with  the  component  A,  the  first  additions  of  B  will  be  dis- 
solved, but  solution  will  no  longer  take  place  beyond  a  certain 
value.  Since  all  solutions  are  soluble  in  one  another  the  same 
reasoning  holds  for  the  constituent  B  as  more  and  more  of  A  is 


FIG.  7. 

added  to  it.  As  soon  as  one  of  the  two  components  is  present  in 
excess  it  is  no  longer  present  as  a  pure  substance,  since  it  con- 
tains some  of  the  other  substance  in  solution.  The  two  liquids 
which  exist  together  under  these  circumstances  without  further 
solution  are  therefore  solutions,  one  of  which  contains  principally 
A  and  the  other  principally  B,  and  both  are  saturated  solutions. 
Laying  off  the  composition  of  the  solutions  along  a  horizontal 
line,  as  in  Fig.  7,  we  will  find  a  point  a  near  A  which  expresses 


SOLUTIONS  127 

the  largest  proportion  of  B  which  can  be  dissolved  in  A.  A  similar 
point  b  will  be  found  near  B,  and  this  expresses  the  largest  pro- 
portion of  A  which  can  be  dissolved  in  B.  All  those  compositions 
which  lie  between  these  points  have  no  existence  as  solutions. 

If  the  two  components  are  brought  together  in  proportions 
lying  between  A  and  a,  a  homogeneous  solution  will  be  formed 
containing  principally  A  and  therefore  similar  to  the  pure  sub- 
stance A.  And  in  the  same  way  a  homogeneous  solution  will  be 
formed  between  B  and  b  having  properties  which  are  similar  to 
those  of  the  pure  substance  B. 

What  will  happen  then  if  the  two  components  are  brought  to- 
gether in  a  relation  like  that  of  c  ?  One  single  solution  cannot  be 
the  result,  and  as  a  matter  of  fact  two  will  form,  the  solution  a 
and  the  solution  b,  and  depending  on  whether  the  relation  of  the 
two  components  lies  nearer  to  a  or  b,  more  of  the  corresponding 
saturated  solution  will  be  formed.  The  relation  ca :  cb  exhibits 
directly  the  relation  between  the  amounts  of  these  two  solutions 
that  will  be  formed. 

Both  solutions  will  be  saturated,  and  this  means  that  they  have 
constant  composition  as  long  as  pressure  and  temperature  remain 
unchanged.  This  agrees  with  the  phase  rule,  for  we  have  dis- 
posed of  two  degrees  of  freedom  in  pressure  and  temperature,  and 
of  two  others  by  assuming  the  existence  of  two  liquid  phases. 
The  number  of  degrees  of  freedom  in  the  case  of  two  components 
is  four.  We  have  therefore  disposed  of  all  of  them,  and  the  com- 
position of  each  phase  must  have  a  fixed  value. 

103.  THE  EFFECT  OF  TEMPERATURE  AND  PRESSURE.  —  The 
limiting  points  a  and  b  are  dependent  on  pressure  and  tempera- 
ture, and  it  is  easy  to  derive  the  following  conclusion  with  the  aid 
of  the  discussion  in  Sec.  67. 

When  liquids  dissolve  one  another  there  is  only  a  small  change 
of  volume,  and  therefore  a  change  of  pressure  will  exert  only  a 
slight  influence  on  the  equilibrium  between  the  solutions.  The 
points  a  and  b  will  therefore  shift  but  little  with  a  change  of  pres- 


128  FUNDAMENTAL  PRINCIPLES  OF  CHEMISTRY 

sure.  The  shift  corresponding  to  an  increase  of  pressure  will  take 
place  in  such  a  way  that  the  pressure  will  decrease,  and  this  means 
that  a  process  which  results  in  a  decrease  of  volume  will  be  set 
up.  In 'the  majority  of  cases  a  decrease  of  volume  accompanies 
the  process  of  solution,  and  when  the  total  volume  is  decreased 
because  one  solution  dissolves  more  of  a  component  of  which  it 
previously  contained  a  smaller  amount,  this  process  will  be  assisted 
by  pressure.  If  the  process  of  solution  in  either  direction  is  ac- 
companied by  an  increase  of  volume,  increased  pressure  will  de- 
crease the  solubility  in  that  direction. 

The  effect  of  temperature  can  be  examined  in  the  same  way. 
An  increase  in  temperature  will  set  up  a  process  which  results  in 
the  absorption  of  heat.  If  a  mutual  increase  in  concentration  cor- 
responds to  this  condition,  such  an  increase  will  result  from  an 
increase  of  temperature,  and  vice  versa.  Both  of  these  cases  have 
been  experimentally  observed,  but  the  first  case  appears  to  be  the 
more  usual  one.  The  mutual  solubility  of  two  liquids  which  are 
only  partially  soluble  in  one  another  generally  increases  with  in- 
creasing temperature. 

It  must  be  kept  in  mind  that  each  of  the  two  points  a  and  b 
can  shift  independently  of  the  other,  for  the  change  of  volume,  or 
the  heat  transfer,  is  not,  in  general,  the  same  for  a  definite  change 
of  concentration  at  a  or  at  6.  A  corresponding  effect  must  there- 
fore be  especially  determined  for  each  of  these  points,  and  it  is  quite 
possible  that  under  a  given  change  of  pressure  one  of  these  points 
will  be  shifted  toward  the  centre  of  the  line  and  the  other  toward 
the  end. 

104.  THE  CRITICAL  POINT  FOR  SOLUTIONS. —  If  we  are  deal- 
ing with  a  pair  of  liquids  of  partial  mutual  solubility,  and  vary 
the  temperature  in  such  a  way  that  the  points  a  and  b  approach 
one  another  closer  and  closer,  they  will  finally  coincide.  The 
region  in  which  two  saturated  solutions  could  exist  becomes  under 
these  conditions  narrower  and  narrower,  and  finally  disappears. 
If  the  change  of  temperature  is  now  carried  further  in  the  same 


SOLUTIONS 


129 


direction  it  will  be  found  that  one  is  dealing  with  liquids  soluble 
in  each  other  in  all  proportions.  We  can  pass  from  the  one  case  to 
the  other  continuously. 

Before  this  point  is  reached  the  following  changes  will  have 
taken  place  in  the  properties  of  the  two  solutions.  The  points  a 
and  b  have  approached  one  another,  and  this  means  that  the  com- 
position of  the  two  solutions  has  become  more  and  more  nearly 
the  same.  When  the  two  points  coincide  this  means  that  the  two 
compositions  have  become  the  same.  We  have  assumed  that 
pressure  and  temperature  were  the  same  in  the  two  solutions; 
they  therefore  exhibit  no  difference  whatever  and  have  become 
alike.  The  surface  of  separation  between  them,  which  existed 
because  the  two  liquids  did 
not  mix,  must  disappear, 
and  both  solutions  will  now 
form  a  homogeneous  liq- 
uid. Fig.  8  is  an  expansion 
of  Fig.  7,  produced  by  plot- 
ting the  coexisting  points 
a  and  b  higher  and  higher 
as  the  temperature  is  in- 
creased, and  this  figure  in- 
dicates the  relations  just 
described. 

We  already  know  of  a 

case  where  two  phases  become  alike  as  a  result  of  continuous 
changes  in  their  properties.  This  was  the  case  of  liquid  and  vapour 
under  constantly  increased  temperature.  The  temperature-pressure 
point  at  which  this  takes  place  we  call  the  critical  point.  Now 
we  can  also  speak  of  a  critical  point  for  solutions,  and  we  under- 
stand by  a  critical  point  one  at  which  two  phases  become  alike. 
This  latter  case  is  somewhat  more  complicated  because  we  are 
now  dealing  with  a  system  of  two  components. 

In  the  previous  case  there  was  only  one  single  critical  point  for 
9 


a 


FIG.  8. 


130  FUNDAMENTAL  PRINCIPLES  OF  CHEMISTRY 

each  substance.  In  a  system  of  one  component  the  sum  of  the 
phases  plus  the  degrees  of  freedom  is  three.  If  vapour  and  liquid 
exist  together  one  degree  of  freedom  is  left,  and  if  we  add  the  con- 
dition that  both  are  to  be  alike  we  have  exhausted  our  last  degree 
of  freedom,  and  there  is  only  one  temperature  and  one  pressure 
which  can  satisfy  the  conditions.  These  are  the  critical  tempera- 
ture and  the  critical  pressure.  Beside  these  we  will  also  have 
determined  a  critical  density  or  critical  specific  volume,  and  with 
this  all  the  characteristics  of  this  point  are  exhausted. 

In  the  case  of  a  critical  point  for  a  solution  we  have  two  phases 
and  the  condition  that  they  are  to  be  alike.  Three  of  our  four 
degrees  of  freedom  are  fixed.  Pressure  is  still  left  free,  and  the 
critical  temperature  of  solution  is  affected  by  a  change  of  pres- 
sure. Or  we  can  choose  the  critical  temperature  of  solution, 
provided  the  pressure  is  fixed  accordingly.  A  large  change  of 
pressure  has  only  a  small  effect  on  the  solubility  of  liquids  and 
therefore  the  change  in  the  critical  temperature  will  be  small. 
Experimentally  it  will  only  be  possible  to  reach  the  critical  temper- 
atures of  solutions  which  correspond  to  pressures  in  the  neighbour- 
hood of  one  atmosphere. 

Instead  of  a  critical  point  in  the  narrow  sense,  we  are  really 
dealing  with  a  critical  line  which  actually  extends  over  a  very 
small  range  of  temperatures  when  the  pressure  is  varied  through 
a  great  range.  Changes  of  this  sort  are  of  about  as  much 
practical  importance  as  the  change  in  the  melting  point  with 
pressure. 

105.  THE  SEPARATION  OF  LIQUID  SOLUTIONS  INTO  THEIR 
COMPONENTS.  —  The  general  reversibility  of  the  process  of  solu- 
tion brings  with  it  the  fact  that  liquid  solutions  can  be  split  up 
into  their  components  as  well  as  built  up  out  of  pure  substances. 
This  is  the  fact,  and  the  process  is  very  much  like  the  separation 
of  a  gaseous  solution  into  its  parts  through  the  agency  of  a  porous 
partition  (Sec.  84),  though  the  means  used  appear  to  be  totally 
different  in  this  case. 


SOLUTIONS  131 

The  separation  of  the  components  of  a  solution  can  be  accom- 
plished by  lowering  the  temperature  until  a  solid  phase  separates. 
We  already  know  that  solid  phases  consist  of  pure  substances  in 
the  great  majority  of  cases,  and  this  gives  us  an  immediate  method 
of  separation.  It  is  much  like  the  application  of  an  ideal  semi- 
permeable  diaphragm  which  permits  of  the  passage  of  only  one 
component,  and  therefore  yields  pure  components  as  a  result  of 
the  separation.  We  have  not  yet  taken  up  the  consideration  of 
equilibrium  between  liquid  and  solid  phases,  and  we  will  there- 
fore leave  this  case  for  later  consideration. 

The  other  possible  method  of  breaking  up  a  solution  into  its 
components  depends  upon  the  production  of  a  gaseous  phase, 
either  by  an  increase  of  temperature  or  a  decrease  of  pressure. 
It  is  experimentally  very  much  easier  to  work  at  high  tempera- 
tures than  it  is  to  work  under  reduced  pressures.  The  first  method 
has  therefore  far  more  general  application,  and  the  second  method 
is  only  used  in  cases  where  an  increase  of  temperature  i-s  to  be 
avoided  for  any  reason.  A  knowledge  of  the  laws  which  describe 
the  corresponding  equilibrium  affords  an  immediate  insight  into 
the  whole  matter. 

106.  THE  VAPOUR  OF  SOLUTIONS.  —  Let  us  consider  the  case 
in  which  a  liquid  solution  is  in  equilibrium  with  its  vapour.  This 
represents  a  combination  of  two  cases  which  we  considered  sepa- 
rately for  the  sake  of  simplicity  in  an  earlier  chapter,  Sections  89 
and  97.  In  the  first  case  we  assumed  that  the  gas  phase  could 
form  a  solution  but  the  liquid  phase  could  not,  and  in  the  other 
case  we  made  use  of  the  reverse  assumption.  It  was  stated  that 
these  assumptions  represent  limiting  cases,  and  that  in  the  general 
case  both  phases  would  form  solutions. 

It  is  usual  to  consider  first  of  all  an  isobaric  relation,  and  this 
means  that  wed£^rn^j^^jj£jf£j^ 


tions  show__the  same  pressure.  Jf  this  pressure  is  one  atmosphere 
the  temperatures  represent  the  ordinary  boiling  points  of  the 
solutions. 


132  FUNDAMENTAL   PRINCIPLES   OF  CHEMISTRY 

Each  of  these  boiling  points  can  be  regarded  as  the  property 
of  a  solution,  and  we  can  then  apply  the  reasoning  used  in  Sec.  100 
in  dealing  with  them.  Each  ^serjesjjf  solutions  containing  the  two 
components  A  and  B  will  possess  a  continuous  series  of  boiling, 
points  lying  between  those  of  the  pure  constituents,  provided  the 
liquids  dissolve  one  another  in  all  proportions,  and  this  we  will 
continue  to  assume  for  the  present.  This  boiling  point  curve  may 
have  any  of  the  forms  shown  in  Fig.  6,  and  all  of  these  have  been 
experimentally  observed. 

I  If  any  solution  is  heated  to  the  boiling  point  its  vapour  will, 
Vn  general,  have  a  different  composition  from  the  liquid.  The 
difference  is  always  of  such  a  nature  that  the  evaporation  results 

_in  a  higher  boiling  point  for  the  residue.  This  is  often  expressed 
fc>y  saying  tnat  the  more  volatile  portion  is  the  first  to  change  into 
vapour,  for  if  the  boiling  point  was  lowered  by  evaporation  the 
vapour  pressure  at  the  existing  temperature  would  soon  become 
greater  than  one  atmosphere  and  further  evaporation  would 
proceed  in  an  explosive  manner.  This  contradicts  our  assump- 
tion that  we  are  dealing  with  an  equilibrium,  and  it  is  a  fact  that 
all  experiments  have  shown  a  rise  in  the  boiling  point  during 
evaporation. 

|Of  course  the  boiling  point  can  only  change  when  the  compo- 
sition of  the  solution  changes/^  If  the  boiling  point  curves  of  neigh- 
bouring solutions  are  examined  one  can  predict  the  direction  in 
which  the  composition  of  a  liquid  solution  will  change  when  it  is 
boiled.  It  will  always  change  toward  that  composition  which 
corresponds  to  a  higher  boiling  point. 

If,  for  example,  we  draw  in  Fig.  6  a  perpendicular  to  the  base 
line  at  the  point  e,  which  represents  the  composition  of  a  solution, 
this  perpendicular  will  cut  the. boiling  point  curves.  Boiling  this 
solution  will  result  in  a  shifting  of  its  composition  toward  the 
right,  when  the  boiling  point  curve  has  one  of  the  forms  a,  b,  or  c, 
and  its  composition  will  be  shifted  toward  the  left  when  the  curve 
has  the  form  d. 


SOLUTIONS  133 

The  composition  of  the  vapour  varies  in  the  opposite  direction, 
for  if  more  of  the  substance  A  is  to  remain  in  the  residue,  more 
of  B  must  have  passed  into  the  vapour. 

If  such  a  solution  is  boiled  it  will  therefore  not  evaporate  at 
constant  temperature  but  at  one  which  increases  constantly  until 
the  last  portion  has  been  volatilized.  Instead  of  a  definite  boiling 
point,  such  as  we  find  in  pure  substances,  we  have  here  a  boiling 
region  corresponding  perfectly  to  the  definition  of  a  solution  which 
we  made  at  the  very  beginning  of  our  discussion  (Sec.  48). 

Similar  relations  are  found  when  the  experiment  is  reversed, 
beginning  with  a  temperature  so  high  that  the  entire  solution  is 
present  in  the  form  of  vapour.  If  it  is  now  cooled  down  step  by 
step  the  first  drop  of  liquid  will  appear  at  a  definite  temperature. 
This  will  not  be  the  temperature  at  which  a  liquid  of  the  same 
composition  begins  to  boil,  but  it  will  be  the  temperature  at  which 
the  last  portion  of  such  a  liquid  evaporated.  We  are  assuming 
in  both  cases  that  vapour  and  liquid  are  continually  in  equilibrium. 
Just  as  we  had  a  region  of  boiling,  we  now  have  a  region  of 
liquefaction,  and  these  two  regions  are  superimposed  just  as 
the  boiling  point  of  a  pure  substance  coincides  with  its  condensa- 
tion point. 

In  order  then  to  describe  the  entire  phenomenon  we  must 
determine  two  temperatures  for  each  composition :  a  lowest  tem- 
perature where  the  first  vapour  can  exist  together  with  the  liquid, 
and  a  highest  one  where  the  first  drops  of  liquid  can  exist  in  the 
presence  of  the  vapour.  Between  these  two  points  lies  the  region 
of  evaporation  and  condensation. 

Every  composition  of  a  solution  corresponds  to  two  such  points 
each  of  which  lies  on  a  continuous  curve.  The  entire  condition 
of  things  is  represented  by  Fig.  9.  The  two  curves  must  coincide 
at  both  ends,  for  the  two  ends  correspond  to  pure  substances,  and 
at  these  points  the  entire  process  of  evaporation  or  condensa- 
tion takes  place  at  a  single  constant  temperature.  In  the  rest  of 
their  course  the  two  lines  are  separated,  and  the  one  correspond- 


134 


FUNDAMENTAL  PRINCIPLES  OF  CHEMISTRY 


ing  to  the  vapour  lies  above  the  one  which  corresponds  to  the 
liquid. 

The  course  of  this  double  line  can  be  determined  in  two  ways 
after  the  boiling  points  have  been  found  as  a  function  of  their 

composition.  One  way  is 
to  transform  a  solution  of 
known  composition  en- 
tirely into  vapour,  meas- 
uring the  temperature  at 
which  the  first  drop  of 
liquid  appears  when  the 
vapour  is  cooled.  This 
gives  a  point  on  the  va- 
pour line  lying  directly 
above  a  corresponding 
point  on  the  liquid  line 
(in  Fig.  9  the  point  d  above 
FlQ-  9-  the  point  /).  Another  way 

is  to  determine  the  com- 
position of  the  first  distillate,  that  is,  of  the  vapour  which  is  in 
equilibrium  with  the  liquid.  This  composition  corresponds  to 
the  lowest  boiling  temperature  of  the  solution,  and  if  the  point  r 
represents  this  composition,  the  intersection  of  a  perpendicular 
erected  at  r,  and  a  horizontal  line  through  the  liquid  point  / 
will  lie  at  the  point  d,  which  is  the  corresponding  vapour 
point. 

It  follows  from  this  construction  that  when  the  two  lines  are 
known,  the  composition  of  all  liquid  and  gaseous  phases  which 
can  exist  in  equilibrium  can  be  determined  by  drawing  horizontals 
through  the  double  line.  Points  cut  by  such  a  horizontal  line 
represent  the  two  compositions  which  are  in  equilibrium. 

This  reasoning  can  be  applied  to  both  cases,  a  and  b,  of  Fig.  6, 
whether  the  boiling  point  curve  is  concave  upward  or  downward. 
If  the  boiling  point  line  exhibits  a  maximum  or  a  minimum,  new 


SOLUTIONS  135 

relations  appear  which  we  shall  examine  immediately.  First  of 
all  let  us  apply  these  general  considerations  to  the  separation  of 
a  liquid  solution  into  its  components. 

107.  DISTILLATION.  —  The  vapour  above  a  liquid  solution  has, 
in  general,  a  different  composition  from  the  liquid  itself.  By 
liquefaction  the  vapour  of  any  solution  can  be  separated  into  two 
fractions  of  different  composition,  and  such  a  separation  is  com- 
plete when  one  of  the  components  possesses  no  measurable  vapour 
pressure,  since  in  this  case  the  vapour  will  consist  of  only  one  of 
the  components.  In  this  case  it  is  only  necessary  to  remove  the 
vapour  continually  as  fast  as  it  is  produced  by  heating  in  order  to 
have  one  component  in  the  residue,  and  the  other  in  the  fraction 
which  has  passed  through  the  vapour  form.  Use  is  made  of  this 
when  pure  water  is  to  be  produced  from  ordinary  river  or  spring 
water.  Ordinary  water  contains  various  substances  which  have 
been  dissolved  out  of  the  earth  while  the  water  was  in  contact 
with  them.  These  substances  have  no  measurable  vapour  pres- 
sure at  the  boiling  point  of  water,  and  when  the  vapour  which  has 
been  produced  from  "impure"  water  is  liquefied,  "pure  water" 
is  produced  which  is  free  from  these  dissolved  substances. 

The  process  by  which  a  liquid  is  changed  into  vapour,  and  the 
vapour  so  formed  is  condensed  to  a  liquid  again,  is  called  distilla- 
tion. In  order  to  carry  out  such  a  process  a  vessel  is  necessary  in 
which  the  liquid  can  be  boiled  and  changed  into  vapour.  Such  a 
vessel  is  usually  called  a  retort.  Beside  this  an  arrangement  for 
condensing  the  vapour  is  necessary,  and  this  is  called  a  condenser. 
In  the  laboratory  these  vessels  are  usually  made  of  glass,  but  in 
technical  work  metal  apparatus  is  employed  because  large  glass 
vessels  are  too  easily  broken. 

The  fact  that  it  is  possible  to  produce  pure  substances  by  dis- 
tillation is  of  great  importance  to  the  chemist,  and  the  discovery 
of  distillation,  which  was  first  practised  in  the  early  middle  ages, 
was  a  very  great  advance  which  assisted  greatly  in  the  study  of 
pure  substances. 


136  FUNDAMENTAL  PRINCIPLES  OF  CHEMISTRY 

108.  FRACTIONAL  DISTILLATION.  —  If  both  constituent^  are 
volatile,  the  separation  resulting  from  a  single  distillation  is  a 
very  incomplete  one,  for  the  two  fractions  which  are  obtained  by 
the  process^^eacti™  conTam  both  components,  present  in  propor- 
tions differing  from  those  of  the  original  substance.  Separation 
can  be  made  practically  complete  by  proper  repetition  of  the 
process  of  distillation. 

The  conditions  here  are  very  similar  to  those  which  have  been 
described  in  Sec.  84  for  the4 separation  of  a  gaseous  solution  by 
a  porous  diaphragm.  When  the  diaphragm  permits  only  one  com- 
ponent to  pass  and  retains  the  other  completely,  this  corresponds 
to  the  case  where  only  one  component  changes  into  vapour.  The 
analogy  extends  also  to  various  degrees  of  permeability  and  vola- 
tility. Two  substances  which  are  under  all  circumstances  alike  in 
their  diffusion  through  diaphragms,  or  in  their  volatility,  could 
not  be  separated  at  all,  but  two  such  substances  could  not  be  dis- 
tinguished from  one  another  at  all,  and  they  would  therefore  be 
the  same  substance.  The  same  directions  as  were  given  in  Sec.  86 
for  the  separation  by  means  of  a  porous  diaphragm  can  be  applied 
to  separation  by  distillation.  The  solution  is  first  of  all  to  be 
separated  by  distillation  into  10  (or  any  other  number)  parts. 
Each  part  is  then  to  be  distilled  again,  and  the  two  halves  kept 
separate,  similar  fractions  being  combined  and  subjected  to  re- 
peated distillation  until  the  whole  solution  has  been  separated 
into  its  components.  In  this  case  also  an  infinite  number  of  dis- 
tillations would  theoretically  be  necessary  to  produce  an  absolute 
separation,  but  long  before  this  point  is  reached  our  means  of  de- 
tecting the  last  remnant  of  the  foreign  component  in  the  nearly 
pure  liquid  would  fail,  and  this  means  that  the  separation  is  prac- 
tically complete. 

The  process  of  separation  by  distillation  can  be  greatly  sim- 
plified by  conducting  it  in  such  a  way  that  the  processes  just 
described  are  carried  on  simultaneously.  This  can  be  done  by 
partially  condensing  the  vapour  as  it  rises  from  the  solution.  The 


SOLUTIONS  137 

solution  so  produced  runs  back  into  the  retort  and  comes  in  con- 
tact with  more  vapour.  In  this  way  it  is  partially  vaporized 
again,  and  the  rising  vapour  contains  more  of  the  more  volatile 
component.  The  less  volatile  component  is  at  the  same  time  con- 
densed and  separated  from  the  vapour,  leaving  a  more  volatile 
fraction  in  the  form  of  vapour.  The  result  is  that  in  a  single  dis- 
tillation a  number  of  successive  distillations  are  carried  on  in  such 
a  way  that  finally  only  the  fraction  with  the  highest  vapour  pres- 
sure remains  in  the  vapour,  while  that  with  the  lowest  vapour 
pressure  is  condensed  and  flows  back  into  the  liquid. 

This  process  is  carried  out  by  causing  the  vapours  to  pass 
through  a  "  distillation  tube/'  in  which  such  a  regular  partial 
condensation  is  produced.  The  technical  arrangement  of  this 
apparatus  varies  with  the  size  of  the  apparatus  in  question.  In 
large  plants  it  usually  consists  of  chambers,  one  above  the  other, 
in  each  of  which  the  temperature  is  regulated  by  cooling  devices. 
In  the  laboratory  a  wide  glass  tube  filled  with  glass  beads  is 
placed  above  the  distilling  vessel,  and  the  heat  of  this  vessel  is  so 
regulated  that  the  tube  is  cooled  sufficiently  by  the  air  about  it  to 
produce  the  desired  result.  It  is  evident  from  the  description  of 
the  process  that  distillation  must  take  place  more  slowly  in  such 
an  apparatus  than  it  does  when  the  vapor  itself  is  condensed, 
since  part  of  the  vapor  is  sent  back  into  the  retort.  A  practical 
separation  is,  however,  attained  in  a  much  shorter  time  with  such 
an  apparatus,  for  a  single  distillation,  accompanied  by  partial  con- 
densation, is  equivalent  to  a  large  number  of  simple  distillations. 

109.  SINGULAR  POINTS.  —  We  have  still  to  discuss  the  question 
how  solutions  behave  whose  boiling  point  passes  through  a  maxi- 
mum or  a  minimum  as  their  composition  changes. 

Let  us  examine  that  portion  of  the  lines  c  and  d  which  lies  to 
the  left  of  the  turning  point  of  the  curves.  It  agrees  with  one  of 
the  two  lines  a  or  b,  neither  of  which  has  any  such  turning  point. 
The  same  is  true  of  the  other  portion  of  these  lines,  and  so  in  this 

HMMHWMST«W^BV 

region  the  composition  of  the  vapour  and  the  residual  liquid  will 


138 


FUNDAMENTAL  PRINCIPLES  OF  CHEMISTRY 


so  change  during  distillation  that  the  residue  will  change  in  com- 
position toward  a  rising  boiling  point,  while  the  distillate  will 
change  inthe  opposite  direction.  But  at  the  singular  point  this 

_-»-ie  "^—       —  J—  l     -  -  -    —  /^x*x"^--V_-—  •  v^.  -  5?^—  ^J.  —  v  ____  ^-— 

will  not  hold,  for  there  the  boiling  points  rise  or  falTon  both  sides.  . 

r<\*  y^^    ->_     ^Vn'^W'  —  '•*"*•'-          -^-—  «-  -=—  •  —  _    -  ^_^~~^J^—  ^.  -  ^—  -*y  -f~—  -^^"^^o** 

The  conclusionto^be^dr^wiij^  ofliquid  and 

vapour  must  be  the  same  at  a  singular 
jpcjmTliaST^^  andsonochange 

in  comosition  caii  result  inthe  formation  of  asoTutiohaving  a 


higKer(or  a  lower)  boilin|^)pjntjlia^^ 

lt6?~SiNGULAR  SOLUTIONS.  —  This  leads  us  to  the  important 
conclusion  that  a  solution  whose  boiling  point  has  the  highest 
(or  lowest)  possible  value  cannot  be  separated  into  its  constitu- 
ents by  distillation,  because  its  vapour  has  the  same  composition 
as  the  liquid.  Such  solutions  behave  in  this  respect  like  pure 
substances. 

In  one  respect  they  are,  however,  very  different  from  pure  sub- 
stances. If  the  boiling  point  curve  for  various  compositions  of 

the  solution  is  plotted  at  other 
pressures,  it  will  be  found 
that,  in  general,  the  singular 
point  corresponds  to  another 
composition.  Boiling  point 
curves  at  various  pressures 
are  shown  in  Fig.  10,  and  it 
is  evident  that  the  maximum 
is  displaced  to  the  right  at 
higher  pressures. 

Although  a  given  solution 
may  behave  like  a  pure  sub- 
stance  when  distilled  at  at- 


. 10. 


mospheric    pressure,   it   will 

behave  like  an  ordinary  solution  at  a  pressure  of  two  atmospheres, 
since  the  vapour  will  be  different  from  the  liquid  residue.  Such 
substances  behave  like  pure  substances  only  at  one  definite  pres- 


SOLUTIONS 


139 


sure  and  at  the  corresponding  temperature.  They  change  their 
state  without  separating  into  two  different  portions,  but  we  will 
nevertheless  classify  them  with  the  solutions.  They  differ  from 
ordinary  solutions  only  in  the  peculiarities  mentioned,  and  we 
shall  therefore  call  them  singular  solutions. 

Such  solutions  were  formerly  classed  with  the  pure  substances, 
but  since  we  have  learned  that  they  behave  like  ordinary  solutions 
at  other  pressures  we  now  call  them  solutions. 

The  behaviour  of  solutions  of  substances  whose  boiling  point 
curve  shows  a  singular  point  can  now  be  accurately  predicted. 
If  thj3cojnj)0j5it^ 

dilation  will  result  in  a  separationjnto^ne_mire  constituent  and 
P3eperSsmithe  composTtio^oithe  solu- 


tion  which  constituejrLwjll/be  sejmialej 
always  be  the  one  which  is 


n 


jjjje^^rjmje^jg^e.     It  will 


of  the  composition  of  the  si 


The  separation  of  such  a  singular  solution  into  its  components 
can  be  effected  by  a  distillation  at  another  pressure.  The  solu- 
tion can  in  this  way  be  separated  into  a  certain  amount  of  one  pure 
constituent  and  another  singular  solution  corresponding  to  the 
new  pressure.  This  latter  portion  may  then  be  distilled  at  the 
original  pressure,  and  it  will  now  behave  like  an  ordinary  solution. 
A  new  separation  results,  some  of  the  other  pure  constituent  being 
formed,  and  the  other  fraction  will  be  the  original  singular  solu- 
tion (but  now  in  less  amount).  By  repeating  the  distillation  alter- 
nately at  the  different  pressures  the  separation  may  be  carried  as 
far  as  desired. 

To  effect  separation  as  rapidly  as  possible  the  pressures  must 
be  as  different  as  possible,  for,  in  general,  the  differences  in  these 
singular  solutions  are  greater  as  the  pressures  are  chosen  further 
apart.  This  will  be  evident  from  Fig.  10. 

These  relations  become  more  evident  if  both  lines,  the  one 
representing  the  composition  of  the  liquids,  the  other  the  com- 
position of  the  vapour,  are  drawn  in  the  way  already  shown  in 


140 


FUNDAMENTAL  PRINCIPLES   OF  CHEMISTRY 


Sec.  106.  Both  phases  have  the  same  composition  at  a  singular 
point.  The  two  lines  must  therefore  have  a  point  in  common  there. 
These  lines  are,  however,  continuous,  and  the  boiling  point  line 
of  the  vapour  must  always  lie  above  that  of  the  liquid.  This 
common  point  can  therefore  not  be  a  point  where  the  curves  cut 

each  other,  but  merely  a  point 
where  they  are  tangent  to  one 
another.  Double  lines  will  re- 
sult like  those  shown  in  Fig.  11. 
As  far  as  this  method  of  repre- 
sentation is  concerned  singular 
solutions  are  like  pure  sub- 
stances. The  double  lines  on 
either  side  of  the  singular  point 
are  in  all  respects  similar  to 
those  of  pure  substances.  It 
may  be  asked  why  phenomena 
of  this  same  type  were  not  men- 
pIG  n  tioned  in  discussing  the  sep- 

aration of  gases  by  means  of 

porous  diaphragms,  provided  such  singular  solutions  ever  occurred 
in  the  case  of  gases.  The  answer  is  that  such  solutions  do  not 
occur  among  gases.  We  concluded  from  the  considerations  in 
Sec.  101  that  if  singular  values  were  to  appear  in  the  proper- 
ties of  a  solution,  these  properties  must  deviate  from  those  which 
could  be  calculated  from  the  simple  rule  of  mixtures.  In  the  case 
of  gases  the  rule  of  mixtures  holds  for  all  properties  and  no  devia- 
tion exists.  The  possibility  that  a  curve  expressing  the  properties 
of  a  gaseous  mixture  should  exhibit  a  maximum  or  a  minimum  — 
a  singular  point  of  any  kind  —  is  therefore  excluded. 

111.  GASEOUS  SOLUTIONS  PRODUCED  FROM  LIQUID  SUB- 
STANCES. —  We  can  now  answer  the  question  of  Sec.  77  whether 
a  gaseous  solution  made  up  of  liquids  can  exist.  Such  a  case  is 
possible  when  the  boiling  point  line  possesses  a  minimum.  In 


SOLUTIONS 


141 


FIG.  12. 


this  case  solutions  will  exist  with  boiling  points  lower  than  those 
of  the  two  constituents.  If  the  constituents  are  mixed  together  at 
a  temperature  which  lies  below  their  boiling  points,  but  above 
this  minimum,  the  solution  will  change  into  vapour,  and  the  change 
will  be  complete  if  the  tem- 
perature is  kept  constant.  All 
the  solutions  which  lie  be- 
tween a  and  b  of  Fig.  12  are 
gaseous  at  the  temperature 
indicated  by  the  line  it,  while 
the  constituents  are  liquid  at 
the  same  temperature.  By 
varying  this  temperature  the 
range  of  existence  of  such 
solutions  can  be  increased  or 
decreased.  This  range  is 

bounded  on  one  hand  by  the  boiling  point  of  the  lower  boiling  con- 
stituent, on  the  other  hand  by  the  boiling  point  of  the  singular 
solution. 

112.  THE  VAPOUR  OF  PARTIALLY  MISCIBLE  LIQUIDS.  —  For 
the  discussion  of  equilibrium  in  the  case  of  two  liquids  which  are 
not  soluble  in  each  other  in  all  proportions,  but  which  form  two 
liquid  phases,  or  two  mutually  saturated  solutions,  let  us  first  con- 
sider the  limiting  case  in  which  the  two  pure  liquids  are  insoluble 
in  each  other.  Strictly  speaking  such  a  case  does  not  exist,  but 
certain  actual  cases  approach  this  so  nearly  as  to  almost  realize 
it.  If  two  liquids  do  not  dissolve  in  one  another  at  all  they  do  not 
influence  each  other,  and  their  vapour  pressure  suffers  no  change. 
If  therefore  two  such  solutions  are  brought  into  an  empty  space, 
each  of  them  will  be  in  equilibrium  with  its  vapour  as  though  the 
other  liquid  were  not  present.  In  other  words,  the  vapour  pres- 
sure of  each  liquid  will  remain  unchanged,  and  the  common 
vapour  pressure  of  the  mixture  will  be  equal  to  the  sum  of  the 
individual  pressures. 


142  FUNDAMENTAL   PRINCIPLES   OF   CHEMISTRY 

As  a  matter  of  fact  all  liquids  must  be  considered  as  soluble  in 
each  other,  and  the  real  question  to  be  answered  is :  what  devia- 
tion from  the  ideal  case  is  brought  about  by  the  solution  of  each  in 
the  other?  The^answer  is.  that  the  vapour  pressure  is  always 
smaller  than  the  sum  of  the  vapour  pressures  of  the  two  indi- 
vidual liquids.  The  partial  pressure  of  each  of  the  liquids  form- 
ing a  solution  is  always  decreased  by  the  formation  of  a  solution, 
and  this  law  holds  without  exception.  If  one  of  the  constituents  of 
the  solution  is  very  slightly  volatile,  so  that  its  vapour  pressure  is 
practically  unmeasurable,  the  decrease  in  the  vapour  pressure  of 
the  other  liquid  is  all  that  is  observed,  and  the  vapour  pressure 
of  the  solution  is  smaller  than  that  of  the  pure  volatile  constituent. 
If  the  second  constituent  has  a  measurable  vapour  pressure  of  its 
own,  the  total  pressure  of  the  solution  may  be  either  smaller  or 
larger  than  that  of  the  more  volatile  constituent.  Whether  one 
or  other  of  these  cases  is  realized  depends  upon  the  effect  of  the 
less  volatile  of  the  constituents  on  the  vapour  pressure  of  the  more 
volatile  one,  and  also  upon  the  difference  in  the  vapour  pressure 
of  the  two  constituents.  If  this  difference  is  large  the  first  case 
may  appear.  The  lowering  of  vapour  pressure  due  to  solution 
may  be  greater  in  amount  than  the  vapour  pressure  of  the  dis- 
solved substance,  and  in  this  case  the  total  pressure  of  the  solu- 
tion will  be  less  than  the  vapour  pressure  of  the  more  volatile 
constituent. 

The  converse  naturally  holds  for  the  boiling  point.  If  the  two 
liquids  do  not  dissolve  one  another  at  all,  the  boiling  point  of  the 
mixture  will  be  lower  than  that  of  the  lowest  boiling  constituent, 
for  boiling  will  begin  when  the  sum  of  the  two  partial  pressures 
equals  the  pressure  of  the  atmosphere.  If  solution  takes  place, 
the  boiling  point  of  the  lower  boiling  constituent  may  be  either 
lowered  or  raised  by  the  addition  of  the  other  substance.  The 
first  case  will  be  realized  by  the  addition  of  a  liquid  having  a  boil- 
ing point  nearly  like  that  of  the  other  liquid.  The  boiling  point 
will  be  raised  by  the  addition  of  liquids  with  a  high  boiling  point. 


SOLUTIONS  143 

These  considerations  can  be  directly  applied  to  the  case  of  two 
liquids  which  are  only  partially  soluble  in  one  another. 

Nothing  further  need  be  said  concerning  conditions  in  the  com- 
mon phase.  The  variable  composition  of  an  unsaturated  solution 
corresponds  to  a  variable  boiling  point,  and  the  corresponding 
double  lines  may  run  either  up  or  down. 

Where  solution  is  incomplete  two  mutually  saturated  liquid 
phases  will  be  formed,  each  possessing  composition  which  does 
not  depend  upon  the  proportions  in  which  the  two  constituents 
were  mixed.  We  must  therefore  conclude  that  the  boiling  points 
of  such  mixtures  of  two  pairs  of  liquids  will  be  constant.  For 
whatever  the  proportions  in  which  the  constituents  are  present,  we 
always  have  two  liquid  phases  of  the  same  composition,  varying 
only  in  the  amount  in  which  each  is  present.  Since  the  amount 
can  have  no  effect  on  the  vapour  pressure  or  the  boiling  point,  it  is 
always  the  same  phases  which  are  boiling,  that  is  to  say,  boiling 
point  and  vapour  pressure  in  the  region  of  saturated  solutions  will 
be  independent  of  the  proportions  in  which  the  constituents  were 
originally  mixed. 

The  same  result  is  reached  by  applying  the  phase  rule.  In  the 
region  in  question  there  are  present  two  liquids  and  a  vapour, 
three  phases  in  all.  The  sum  of  phases  and  degrees  of  freedom 
is  in  this  case  four,  and  there  therefore  remains  one  degree  of 
freedom.  If  the  temperature  is  fixed  the  entire  condition  of  the 
system  is  determined  and  nothing  is  changed  by  a  change  in  pro- 
portions, that  is  to  say,  the  pressure  is  independent  of  the  propor- 
tions in  which  the  two  components  are  present.  If  the  pressure 
is  fixed  the  temperature  will  be  also  independent  of  the  proportions. 
If  we  now  draw  the  boiling  point  line  representing  all  possible  re- 
lations of  the  constituents,  this  describes  the  intermediate  region 
in  which  two  liquid  phases  can  exist  together,  and  it  will  be  a  hori- 
zontal straight  line,  for  such  a  line  means  that  a  mixture  containing 
every  possible  proportion  of  the  two  constituents  will  have  the 
same  boiling  point. 


144  FUNDAMENTAL   PRINCIPLES   OF  CHEMISTRY 

The  two  saturated  liquid  solutions  which  can  exist  together  as 
two  phases  in  all  proportions  we  will  call  limiting  solutions.  It 
should  be  noticed  that  the  boiling  point  and  the  vapour  pressure 
of  each'  limiting  solution  by  itself  must  be  the  same  even  though 
the  other  phase  is  not  present.  These  points  we  have  found  to 
be  the  same  when  one  of  the  liquid  phases  was  present  with  any 
amount  of  the  other,  however  small.  It  is  therefore  possible  to 
approach  the  condition  in  which  only  one  of  the  liquids  is  present 
as  closely  as  we  desire  without  causing  any  change  in  the  vapour 
pressure.  The  law  of  continuity  demands  that  at  the  moment 
when  one  or  the  other  of  the  liquids  disappears  the  vapour  pressure 
must  still  remain  the  same. 

The  same  conclusion  may  be  reached  in  a  different  way  by  the 
use  of  the  general  principle :  A  system  which  is  in  equilibrium  in 
one  sense  is  in  equilibrium  in  every  sense. 

We  have  already  made  use  of  this  principle  to  show  that  the 
vapour  pressure  of  ice  must  be  the  same  as  that  of  water  when 
these  two  substances  are  in  equilibrium;  since  otherwise  one  of 
the  phases  must  increase  at  the  expense  of  the  other,  which  contra- 
dicts the  assumption  of  equilibrium.  In  this  case  also  we  must 
conclude  that  when  the  two  liquids  do  not  affect  one  another  while 
they  are  in  direct  contact,  they  cannot  do  so  in  any  indirect  way. 
Suppose  our  two  limiting  solutions  to  exist  side  by  side  in  two 
vessels  covered  with  a  bell-jar  filled  with  their  vapour.  .If  the 
vapor  pressure  of  one  of  these  limiting  solutions  is  greater  than 
that  of  the  other,  a  distillation  from  one  to  the  other  will  take  place ; 
that  is  to  say,  the  system  is  not  in  equilibrium.  In  the  same  way 
it  can  be  shown  that  not  only  the  total  vapour  pressure  above  each 
solution  must  be  the  same,  but  also  that  the  partial  pressure  of 
the  two  constituents  must  be  the  same ;  for  if  they  were  not  the 
same  a  distillation  would  result,  and  in  this  case  it  would  be  a 
distillation  from  both  directions.  In  one  of  the  liquids  the  vapour 
pressure  of  A  would  be  greater  and  in  the  other  B,  since  the  sum 
of  the  two  has  already  been  shown  to  be  the  same.  A  would  there- 


a 


SOLUTIONS  145 

fore  distil  from  one  vessel  to  the  other,  and  B  would  distil  in  the 
opposite  direction.  Both  liquids  would  under  these  circumstances 
change  in  composition,  which  is  again  a  contradiction  of  our  as- 
sumption of  equilibrium. 

113.  POSSIBLE  CASES. — The  vapour  pressure  and  boiling 
point  lines,  which  describe  the  regions  between  the  limiting  solution 
and  the  pure  constituents, 
will  have  a  regular  course 
from  the  ends  of  the  hori- 
zontal straight  line,  repre- 
senting the  limiting  solution, 
to  the  values  for  the  pure 
constituents.  Three  cases  are 
possible,  and  they  are  repre- 
sented by  the  lines  a,  6,  and  c 
of  Fig.  13.  It  can  be  shown 
that  only  a  and  b  can  occur, 
while  c  includes  a  contra-  FIG.  13. 

diction. 

Let  us  consider  first  of  all  a  in  Fig.  13,  which  represents  boiling 
point  lines.  From  earlier  considerations  we  know  that  the  vapour 
has  a  composition  which  is  different  from  that  of  the  liquid,  as 
shown  by  the  drop  at  the  beginning  of  the  boiling  point  line.  The 
composition  of  the  vapour  from  the  left-hand  limiting  solution  will 
lie  to  the  right  of  this  point  and  that  of  the  vapour  from  the  right- 
hand  limiting  solution  will  lie  to  the  left  of  its  composition.  Both 
vapours  have  the  same  composition,  as  has  just  been  proven,  and 
so  the  composition  of  the  vapour  must  be  represented  by  some 
point  between  the  two  limiting  solutions.  If  one  of  the  limiting 
solutions  is  distilled,  the  distillate  will  consist  of  two  fractions, 
each  of  them  a  limiting  solution,  and  of  course  the  same  will  hold 
true  if  any  given  mixture  of  the  two  limiting  solutions  is  distilled, 
for  the  vapour  in  this  case  will  be  exactly  the  same  as  before. 

If  we  apply  the  same  reasoning  to  the  case  b  we  find  that  the 
10 


146  FUNDAMENTAL   PRINCIPLES   OF  CHEMISTRY 

vapour  of  the  right-hand  limiting  solution  must  have  a  composi- 
tion represented  by  a  point  which  lies  to  the  left  of  the  limiting 
solution  point.  In  the  case  of  the  left-hand  limiting  solution  we 
find  however  a  different  result  from  that  of  the  former  case.  The 
composition  of  the  vapour  must  lie  to  the  left  of  the  limiting  solu- 
tion, for  there  the  boiling  points  drop  to  the  left,  and  the  composi- 
tion of  the  vapour  must  always  differ  from  that  of  the  liquid  in 
the  direction  of  decreasing  vapour  pressure.  We  must  therefore 
conclude  that  in  this  case  the  vapour  will  have  a  very  one-sided 
composition,  for  the  proportions  of  the  two  constituents  in  it  are 
represented  by  a  point  which  lies  far  to  the  left.  This  composition 
lies  outside  the  two  limiting  solutions  in  a  region  where  the  two 
liquids  give  a  homogeneous  solution,  and  to  the  side  belonging  to 
the  more  volatile  liquid.  If  either  of  the  limiting  solutions  be  dis- 
tilled the  distillate  will  not  in  this  case  separate  into  two  layers,  but 
will  be  homogeneous,  and  will  contain  a  large  proportion  of  the 
volatile  constituent. 

In  the  case  c  the  same  considerations  lead  us  to  the  result  that 
the  left-hand  limiting  solution  would  yield  a  distillate  of  composi- 
tion lying  to  the  left  of  that  of  the  limiting  solution,  while  the  right 
yields  a  distillate  whose  composition  lies  to  the  right.  These  two 
conditions  are  impossible  of  fulfilment,  and  such  a  system  is  there- 
fore an  impossible  one.  As  a  matter  of  fact  only  the  two  cases  a 
and  b  have  ever  been  observed. 

114.  THE  DOUBLE  LINE.  — These  considerations  are  extended 
and  confirmed  when  the  double  line,  which  includes  the  composi- 
tion of  the  vapour  phase,  is  used  in  place  of  the  single  line  in  repre- 
senting the  boiling  points  based  upon  the  composition  of  the  liquid 
phase  alone.  It  has  been  shown  that,  in  general,  the  line  cor- 
responding to  the  vapour  must  lie  above  that  of  the  liquid,  and  in 
Fig.  14  there  is  represented  the  case  a  with  the  addition  of  the 
vapour  line,  which  lies,  as  it  should,  above  the  liquid  line.  First 
it  should  be  noticed  that  this  line  must  be  everywhere  a  curved 
one.  Since  vapours  are  soluble  in  one  another  in  all  proportions, 


SOLUTIONS 


147 


FIG.  14. 


no  horizontal  parts  can  ever  appear  like  those  which  correspond 
to  the  appearance  of  two  liquid  pairs  when  liquids  are  mixed. 
Beside  this  the  vapour  line  must  touch  the  horizontal  part  of  the 
liquid  line  between  the  two  limiting  solutions,  for  the  two  limiting 
solutions  send  out  vapour  of  the  same  composition,  which  can 
be  condensed  to  a  definite 
mixture  of  the  two  liquid 
phases.  This  mixture  when 
boiled  must  therefore  send 
out  a  vapour  having  the 
same  composition,  and  it  can 
therefore  be  transformed  into 
vapour  completely  without 
any  change  in  the  boiling 
point.  This  particular  mix- 
ture behaves  in  this  respect 
like  a  pure  substance,  for  it 
has  a  definite  boiling  point 

and  not  a  boiling  region  like  the  solutions.  At  this  point  there- 
fore the  vapour  line  must  have  a  point  in  common  with  the 
horizontal  liquid  line,  that  is,  it  must  be  tangent  to  it. 

In  earlier  cases,  Sec.  110,  we  found  that  singular  solutions  could 
exist.  In  this  case  we  find  a  singular  mixture  of  two  liquid  phases 
which  behaves  like  a  pure  substance  during  vaporization. 

It  is  immediately  evident  that  this  distillate  is  a  mixture,  and 
there  is  no  difficulty  whatever  in  distinguishing  such  a  singular 
mixture  from  a  pure  substance  in  spite  of  its  constant  boiling 
point.  We  will  find  later,  when  we  come  to  the  consideration  of 
solid  bodies,  that  there  may  be  analogous  cases  where  it  is  by  no 
means  so  easy  to  decide  this  point,  and  we  shall  find  that  the  con- 
siderations just  discussed  will  be  of  help  to  us  in  this  later  case. 

The  composition  of  such  a  singular  mixture  is,  in  general, 
variable  with  the  temperature,  and  this  affords  a  further  means  of 
distinguishing  such  a  mixture  from  a  pure  substance. 


148 


FUNDAMENTAL   PRINCIPLES   OF  CHEMISTRY 


In  the  case  6,  Fig.  13,  no  singular  mixture  appears,  for  the  com- 
position of  the  vapour  lies  outside  the  region  included  between 
the  two  limiting  solutions,  so  that  the  distillate  is  not  a  mixture 
but  an  unsatu rated  solution.  This  solution  has,  however,  a  con- 
stant composition  as  long  as  both  liquid  phases  are  present.  The 
composition  of  this  distillate  lies  so  far  to  one  side  that  no  mixture 
can  exist  which  can  be  distilled  entirely  without  a  change  in  the 
boiling  point.  If  such  a  mixture  could  exist  it  would  be  a  singular 
mixture.  In  this  case  the  larger  proportion  of  the  vapour  will  be 
made  up  of  the  lower  boiling  constituent,  and  after  distillation  has 
proceeded  for  a  time  there  will  remain  only  the  limiting  solution 
which  is  richer  in  the  higher  boiling  constituent,  and  its  composi- 
tion will  vary  by  further  distillation  and  with  a  corresponding  rise 

in  the  boiling  point  toward  a 
greater  and  greater  content  of 
the  less  volatile  constituent. 

In  Fig.  15  the  vapour  pres- 
sure line  is  added  above  the 
liquid  line  corresponding  to  b 
of  Fig.  13.  The  composition 
of  the  distillate  is  found  by 
continuing  the  horizontal  part 
of  the  liquid  line  until  it  cuts 
the  vapour  line  at  the  point  d. 
It  is  evident  from  the  con- 
ditions shown  by  the  diagram 

that  this  composition   must  always  lie  far  to  one  side,  that  is,  it 
represents  a  high  percentage  of  one  or  other  of  the  constituents. 

115.  EQUILIBRIUM  WITH  SOLID  SUBSTANCES. — The  state  in 
which  the  constituents  of  a  solution  exist  before  solution  can  of 
course  have  nothing  to  do  with  the  properties  of  the  solution  itself. 
No  special  relations  are  to  be  expected  in  solutions  themselves, 
but  special  relations  do  exist  in  mixtures  where  a  solid  phase  is 
present.  The  following  general  considerations  should  be  kept 


FIG.  15. 


SOLUTIONS  149 

in  mind.  Equilibrium  between  solid  phases  is  usually  simpler 
than  between  liquids,  because  solid  substances  do  not,  as  a  rule, 
form  solid  solutions.  They  are  generally  pure  substances,  and 
they  usually  remain  so  even  when  other  solids  are  present.  The 
result  is  that  in  such  systems  only  one  of  the  phases  exhibits  the 
variable  character  of  a  solution,  while  the  other  phase  has  a  con- 
stant composition  and  therefore  constant  properties.  This  holds 
primarily  for  a  liquid  phase,  but  in  the  case  of  gases  also  simplify- 
ing conditions  prevail  because  the  majority  of  solid  substances 
do  not  possess  a  measurable  vapour  pressure.  The  vapour  pres- 
sure of  such  solutions  consists  therefore  almost  entirely  of  a  single 
constituent,  and  the  laws  which  describe  the  conditions  in  such  a 
system  are  simpler  than  they  would  be  if  the  vapour  also  had  to 
be  considered  as  a  solution.  In  other  words,  we  should  have  to 
deal  with  specially  simple  phenomena  of  saturation. 

In  general,  when  a  solid  substance  is  placed  in  a  liquid  it  is 
dissolved,  that  is  to  say,  a  liquid  solution  is  formed.  When  the 
amount  of  the  solid  added  is  small,  the  properties  of  the  solution 
are  very  similar  to  those  of  the  liquid  substance  or  solvent.  As  is 
in  general  the  case  for  solutions,  they  may  exhibit  all  possible 
values  of  their  properties,  varying  with  the  composition  and 
bounded  by  certain  definite  limits.  In  this  respect  these  solutions 
are  in  no  way  different  from  others. 

If  the  amount  of  the  solid  substance  is  increased  beyond  a  cer- 
tain limit,  it  will  no  longer  be  dissolved  but  will  remain  as  a  solid 
in  contact  with  the  solution.  It  is  customary  to  call  such  a  solu- 
tion which  exists  in  contact  with  another  phase  a  saturated  one, 
and  it  is  said  to  be  saturated  with  respect  to  the  solid  substance. 
The  solution  has  taken  on  a  definite  composition  and  definite  prop- 
erties, and  a  further  increase  in  the  amount  of  the  solid  phase  has 
no  effect  on  these.  This  corresponds  to  the  general  case  of  equilib- 
rium between  several  phases,  for  such  an  equilibrium  is  independ- 
ent of  the  relative  and  absolute  amounts  of  the  phases  concerned. 

The  proportions  of  liquid  and  solid  corresponding  to  saturation 


150  FUNDAMENTAL  PRINCIPLES   OF  CHEMISTRY 

are  dependent  in  the  first  place  upon  the  nature  of  the  two  sub- 
stances. There  are  many  cases  where  the  solubility  is  so  small 
(that  is,  .where  the  amount  of  the  solid  which  corresponds  to  equi- 
librium in  the  solution  is  so  small)  that  there  can  be  doubt  whether 
there  has  been  solution  at  all.  Of  late  years,  however,  improved 
means  for  recognising  small  amounts  of  dissolved  substances  (by 
measurement  of  electrical  conductivity,  for  example)  have  shown 
that  many  substances  previously  considered  to  be  insoluble  really 
possess  a  definite,  though  of  course  very  slight,  solubility.  We  have 
therefore  reason  to  assume  that  a  small  but  finite  solubility  exists 
in  all  cases,  even  though  it  has  not  been  experimentally  proven. 

In  the  condition  of  saturation  the  liquid  solution  exhibits  a 
definite  relation  between  the  original  liquid  (which  can  in  this 
case  be  designated  as  solvent,  although  both  components  take 
part  in  the  formation  of  a  solution)  and  the  dissolved  solid  sub- 
stance. This  relation  is  usually  expressed  in  per  cent,  indicating 
the  number  of  parts  by  weight  of  the  solid  substance  which  are 
contained  in  100  parts  by  weight  of  the  solution.  Saturation  is 
sometimes  expressed  in  parts  by  weight  of  solid  to  100  parts  of 
solvent,  but  since  the  first  method  of  expression  is  the  best,  we 
shall  always  make  use  of  it  to  the  exclusion  of  the  other. 

116.  THE  EFFECT  OF  PRESSURE  AND  TEMPERATURE. — The 
condition  of  saturation  leaves  two  degrees  of  freedom.  The  sum 
of  the  phases  and  degrees  of  freedom  is  four  for  two  constituents, 
and  when  only  two  phases  are  present  two  degrees  of  freedom  re- 
main. A  change  in  the  proportions  of  saturation  with  temperature 
and  pressure  must  therefore  be  expected.  As  far  as  the  effect  of 
pressure  is  concerned,  it  must  be  kept  in  mind  that  the  change  in 
volume  accompanying  the  formation  of  a  solution  from  a  liquid 
and  a  solid  substance  is  usually  very  small.  A  decrease  in  volume 
is  the  usual  case,  but  occasionally  we  find  an  increase.  In  the 
first  case  an  increase  of  pressure  at  constant  temperature  will 
cause  an  increase  in  the  solubility.  In  the  second  case  it  will  cause 
a  decrease,  but  the  effect  is  so  small  that  it  is  difficult  to  measure, 


SOLUTIONS  151 

and  practical  interest  in  the  effect  is  satisfied  with  the  proof  that 
the  change  takes  place  in  the  direction  indicated  by  the  theory. 

Similar  considerations  hold  for  the  effect  of  temperature  at  con- 
stant pressure.  The  solution  of  solid  bodies  in  liquids  may  take  place 
either  with  absorption  of  heat  or  with  the  opposite  result,  according 
to  the  nature  of  the  substances,  that  is,  either  with  an  increase  or  a 
decrease  in  the  entropy  of  the  system,  and  a  corresponding  effect 
of  temperature  on  the  equilibrium  must  be  expected.  Those  sub- 
stances which  absorb  heat  during  solution  (this  is  indicated  by  a  de- 
crease of  temperature  during  solution)  increase  their  solubility  with 
increasing  temperature,  and  vice  versa.  This  principle  has  been 
confirmed  by  experiment  in  a  very  great  number  of  individual  cases. 

Attention  must  here  be  called  to  special  conditions  which  make 
this  matter  somewhat  more  complicated  than  appear  in  the  state- 
ment just  given.  The  amount  of  heat  which  accompanies  solu- 
tion is  not  independent  of  the  concentration  itself.  If,  for  example, 
equal  amounts  of  saltpetre  are  added,  one  after  the  other,  to  a 
given  amount  of  water,  the  solution  of  the  first  portion  of  the  salt 
in  pure  water  will  be  accompanied  by  the  absorption  of  a  larger 
amount  of  heat  than  is  absorbed  by  the  addition  of  the  second 
amount  of  the  salt,  and  the  third  portion  corresponds  to  still  less 
heat  absorbed.  But  the  principle  upon  which  the  above  rule  is 
based  holds  only  for  equilibrium  and  for  a  change  in  equilibrium. 
The  direction  of  the  change  in  equilibrium,  due  to  a  change  in 
temperature,  is  to  be  found  by  answering  the  question :  what  amount 
of  heat  is  taken  in  or  given  out  by  the  system  during  a  change  in 
equilibrium f  We  must  choose  that  particular  value  for  the  heat 
of  solution  which  corresponds  to  saturation.  In  other  words,  we 
must  determine  what  heat  change  takes  place  when  the  saturated 
solution  takes  up  or  loses  a  given  amount  of  the  salt.  This  problem 
appears  at  first  glance  to  be  insoluble ;  but  there  are  several  ways 
of  reaching  an  approximate  solution,  and  it  is  only  when  these 
relations  have  been  taken  into  account  that  complete  agreement 
between  theory  and  observation  has  been  found. 


152 


FUNDAMENTAL   PRINCIPLES  OF  CHEMISTRY 


A  general  idea  of  the  effect  of  temperature  on  solubility  can  best 
be  obtained  by  a  diagrammatic  representation  such  as  the  one 
used  in  Sec.  104  to  represent  conditions  in  solutions  of  liquids. 
The  diagram  is  simpler  in  this  case  since  only  one  concentration 
corresponds  to  each  temperature,  while  in  the  former  case  we  had 
two.  The  solid  phase  does  not  dissolve  a  measurable  amount  of 
the  liquid,  and  we  need  only  to  represent  the  concentration  of  the 
liquid  solution. 

In  the  majority  of  cases  such  solubility  diagrams  are  very  nearly 


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CONCENTRA  TION 

FIG.  16. 

straight  lines.  Fig.  16  shows  the  solubility  line  of  saltpetre  in  water. 
Furthermore  such  a  line  is  always  a  continuous  one  as  long  as  the 
properties  of  the  solid  phase  suffer  no  change. 

117.  LIQUID  SOLUTIONS  OF  SOLID  SUBSTANCES.  —  A  solution 
of  salt  in  water  freezes  at  a  lower  temperature  than  pure  water. 
If  therefore  ice  at  0°  is  mixed  with  salt  these  two  solid  substances 
turn  into  liquid  and  the  result  is  a  liquid  solution,  —  a  solution  of 
salt  and  water. 

This  behaviour  is  a  general  one.     With  a  very  few  exceptions 


SOLUTIONS 


153 


(which  have  their  cause  in  the  formation  of  solid  solutions)  the 
melting  point  of  a  solid  substance  is  lowered  when  it  is  not  in  con- 
tact with  its  own  pure  liquid,  but  is  placed  in  contact  with  any 
liquid  solution  of  which  it  either  forms  or  can  form  a  constituent. 
The  melting  point  in  this  case  does  not  correspond  to  equilibrium 
between  a  solid  and  a  pure  liquid,  but  to  equilibrium  between  a 
solid  and  a  solution.  The  lowering  of  the  melting  point  is  greater 
the  greater  the  content  of  this  solution  in  dissolved  substance,  and 
the  lowering  could  go  on  indefinitely  if  it  were  not  limited  by  cor- 


a 


FIG.  17. 

responding  conditions  determining  the   behaviour  of   the  other 
solid  substance  and  its  solution. 

In  Fig.  17,  a  represents  the  melting  point  of  the  pure  substance  A, 
temperature  being  as  usual  plotted  upward  and  composition  hori- 
zontally. Solutions  of  A  and  B,  represented  according  to  their 
composition  as  lying  between  A  and  B,  will  have  melting  points 
which  lie  lower  as  the  composition  of  the  solution  is  further  from 
the  point  A.  Experience  has  shown  that  this  lowering  of  the  melt- 


154  FUNDAMENTAL   PRINCIPLES   OF  CHEMISTRY 

ing  point  is  nearly  proportional  to  the  amount  of  B  which  is  present 
in  the  solution,  and  this  means  that  the  line  ok  is  nearly  straight. 

Precisely  similar  considerations  are  to  be  applied  for  the  second 
substance  B  whose  melting  point  lies  at  6,  at  a  distance  above  B, 
which  may  be,  according  to  circumstances,  greater  or  less  than  a 
above  A.  For  the  melting  point  of  B  in  contact  with  solutions 
which  contain  the  substance  A  dissolved  in  B  we  will  find  a  line 
running  downward  like  bk.  If  both  these  lines  are  followed  fur- 
ther and  further  they  will  finally  cut  one  another  at  a  point  k.  Let 
us  discuss  the  meaning  of  the  point  k. 

The  line  ak  represents  equilibrium  conditions  between  solid  A 
and  liquid  solutions  of  A  and  B.  The  line  bk  represents  equilib- 
rium between  solid  B  with  liquid  solutions  of  A  and  B.  These 
solutions  are  the  same  as  those  in  the  previous  case,  the  only 
difference  being  that  now  B  is  present  in  greater  percentage,  while 
in  the  first  case  A  made  up  the  greater  part.  The  point  k  belongs 
to  both  lines,  it  is  therefore  characteristic  of  a  temperature  and  a 
composition  such  that  both  solid  A  and  solid  B  are  in  equilibrium 
with  a  solution  of  definite  composition.  At  this  point  three  phases, 
two  solid  and  one  liquid,  are  coexistent.  One  degree  of  freedom 
remains,  and  either  the  pressure  or  the  temperature  can  be  arbi- 
trarily chosen.  In  general  the  formation  of  a  liquid  solution  from 
solid  A  and  solid  B  is  accompanied  by  a  very  slight  change  of 
volume.  The  change  in  this  equilibrium  point  with  pressure  will 
therefore  be  very  slight,  and  it  is  in  fact  so  slight  that  it  is  difficult 
to  show  experimentally.  We  may  therefore  leave  this  variable 
out  of  consideration  for  the  present,  and  we  must  conclude  that 
there  is  a  definite  temperature  and  a  definite  composition  depend- 
ent only  on  the  nature  of  the  two  solid  substances  A  and  B,  at 
which  a  solution  of  these  two  substances  can  exist  in  equilibrium 
with  both  solids.  It  will  also  be  noticed  that  this  temperature  is 
the  lowest  at  which  one  of  the  two  substances  can  be  in  stable 
equilibrium  with  the  solution  containing  both.  Equilibria  at  tem- 
peratures lower  than  this  are  not  necessarily  excluded,  and  if  the 


SOLUTIONS  155 

presence  of  solid  B  is  avoided,  the  line  ak  can  be  observed  for 
some  distance  beyond  k,  as  indicated  by  the  dotted  prolongation 
in  the  figure,  while  similar  reasoning  holds  for  the  prolongation  of 
bk.  Such  states  are  unstable ;  they  are  first  of  all  metastable,  and 
become  labile  if  the  line  is  carried  further.  If  we  confine  ourselves 
to  states  of  complete  stability,  k  is  definitely  the  lowest  point  of 
equilibrium  between  the  solid  and  liquid  forms  of  A  and  B. 

118.  THE  EUTECTIC  POINT.  —  If,  therefore,  a  solution  of  com- 
position K  is  made  to  freeze  by  the  introduction  of  a  trace  of  both 
solids  A  and  B,  the  temperature  cannot  sink  lower  than  k,  no 
matter  how  much  of  the  solution  freezes;  and  this  is  true  because 
k  is  the  lowest  temperature  at  which  the  two  substances  in  the 
solid  state  can  exist  in  the  presence  of  their  solution.  Nor  can 
the  temperature  rise,  for  by  the  separation  of  a  solid  constituent 
from  a  solution  the  temperature  can  only  sink.  If  the  temperature 
could  rise  under  these  circumstances  equilibrium  would  be  im- 
possible. The  only  thing  that  can  happen  is  that  the  temperature 
must  remain  constant.  This  brings  with  it  the  condition  that  in 
spite  of  the  separation  of  a  solid  from  the  solution  the  composition 
of  the  solution  must  remain  constant.  If  this  condition  is  to  be 
fulfilled,  the  two  solid  substances  must  freeze  out  of  the  solution 
as  a  mixture  having  the  same  composition  as  the  solution  with 
which  it  is  in  equilibrium.  As  far  as  this  one  property  is  con- 
cerned this  solid  mixture  behaves  like  a  pure  substance,  for  it  is 
formed  from  its  solution  at  constant  temperature,  and  remains  at 
exactly  the  same  constant  temperature  k  all  the  time  it  is  melting. 

A  solution  of  composition  K  which  freezes  in  such  a  way  that 
a  constant  solid  mixture  of  A  and  B  separates  is  called  a  eutectic 
solution,  and  the  solid  mixture  is  called  a  eutectic  mixture.  The 
temperature  k  is  called  the  eutectic  temperature,  and  the  point  k 
which  characterizes  composition  and  temperature  is  called  the 
eutectic  point.  The  eutectic  solution  behaves  towards  its  eutectic 
mixture  like  a  pure  substance,  since  it  no  longer  exhibits  the 
changing  freezing  point  which  is  characteristic  for  solutions. 


156  FUNDAMENTAL   PRINCIPLES   OF  CHEMISTRY 

If  any  solution  which  has  not  the  same  composition  as  the  eu- 
tectic, but  which  contains,  for  example,  a  larger  amount  of  the 
substance  A,  is  made  to  freeze,  the  substance  A  separates  in  the 
solid  form.  The  liquid  solution  becomes  therefore  richer  in  B, 
and  its  freezing  point  is  lowered.  This  process  goes  on  as  more 
heat  is  taken  away;  the  freezing  point  becomes  lower  and  lower, 
and  if  subcooling  is  avoided  it  sinks  until  the  eutectic  point  is 
reached.  From  this  time  on  it  remains  constant.  A  does  not  sepa- 
rate alone  from  the  solution,  and  the  solid  which  separates  is  now 
the  eutectic  mixture  of  A  and  B.  The  same  holds  for  solutions 
with  an  excess  of  B,  but  in  this  case  pure  B  separates  first 
and  the  eutectic  mixture  follows. 

This  behaviour  brings  to  mind  the  singular  solutions  with  a 
maximum  or  minimum  of  the  boiling  point  (Sec.  109).  There 
also  we  had  a  definite  solution  and  a  vapour  of  the  same  composi- 
tion as  a  liquid,  behaving  so  far  like  a  pure  substance.  There  is, 
however,  a  difference  to  be  noticed,  for  in  the  previous  case  we 
were  considering  equilibrium  between  two  solutions,  one  liquid 
and  one  gaseous,  both  having  the  same  composition.  Here  we 
are  dealing  with  a  liquid  solution  on  the  one  hand  and  with  a 
solid  mixture  on  the  other.  It  is  easier  therefore  to  determine  the 
difference  between  a  eutectic  mixture  and  a  pure  substance  than 
it  was  in  the  first  case,  where  we  had  to  do  with  a  liquid  and  a 
gaseous  solution. 

For  if  the  solid  phase  is  a  mixture,  the  laws  which  hold  true 
for  mixtures,  and  especially  those  which  describe  the  relation  be- 
tween the  properties  of  the  constituents  and  those  of  the  mixture, 
must  be  in  evidence.  Experiments  made  on  this  point  have  proven 
that  eutectic  mixtures  are  true  mixtures  with  respect  to  all  their 
properties,  that  is,  it  is  possible  to  calculate  their  properties  from 
those  of  their  constituents  by  means  of  the  law  of  mixtures. 

1 19.   CONNECTION  WITH  THE  ORDINARY  SOLUBILITY  CURVE.  - 
Let  us  inquire  into  the  connection  between  the  relationship  just 
explained  and  the  curve  of  Sec.  117,  which  represents  the  variation 


SOLUTIONS 


157 


in  the  solubility  of  a  solid  substance  with  the  temperature.  It 
will  be  found  that  we  are  dealing  with  a  piece  of  one  of  the  two 
lines  leading  from  the  melting  points  to  the  eutectic  point.  In  the 
majority  of  solutions  of  various  salts  in  water  one  of  the  melting 
points  (that  of  the  salt)  usually  lies  so  high  that  the  vapour  pres- 
sure of  the  solution,  made  up  of  a  large  percentage  of  liquid  salt 
and  a  small  percentage  of  water,  is  very  high  indeed.  Solutions 
of  this  sort  are  very  difficult  to  make  and  to  observe,  and  we  know 
but  very  little  about  them. 


350° 

30(f 

25O° 

200° 

15O° 

/OO° 

50° 

ff 


m 


u      jo 


30 


4O       3O 

FIG.  18. 


7O       8O       9O      IOO 


On  the  other  hand,  the  solubility  of  a  salt  at  temperatures  below 
zero  is  often  small,  and  it  is  only  infrequently  that  any  practical 
interest  exists  in  the  equilibrium  between  such  a  solution  and  ice. 
It  is  for  this  reason  that  the  region  in  which  solid  water  (ice)  is 
in  equilibrium  with  the  liquid  solution  has  also  remained  unknown 
in  the  majority  of  cases. 

Let  us,  for  example,  extend  Fig.  16  so  that  all  the  equilibria 
between  saltpetre  and  water  appear  in  it.  In  Fig.  18  this  has 


158  FUNDAMENTAL   PRINCIPLES   OF  CHEMISTRY 

been  done,  and  we  have  from  a  to  k  the  composition  of  such  salt- 
petre solutions  as  are  in  equilibrium  with  ice  at  the  corresponding 
temperatures.  These  are,  in  other  words,  the  freezing  points  of 
these  solutions  of  saltpetre.  The  eutectic  point  corresponds  to 
a  content  of  10.9  parts  of  salt  in  100  parts  of  solution,  and  lies  at 
—  2.9°.  From  that  point  on  we  have  equilibria  between  liquid 
solution  and  solid  salt  to  the  melting  point  of  the  salt,  which  lies 
at  331°,  and  these  points  lie  between  k  and  6.  This  branch  of  the 
curve  corresponds  to  the  solubility  curve  ku  of  Fig.  16,  and  in 
order  to  make  it  more  evident  it  is  drawn  as  a  heavy  line.  The 
region  between  u  and  b  we  know  nothing  about,  for  reasons  already 
mentioned.* 

120.  SOLUBILITY  AT  THE  MELTING  POINT.  —  When  a  solid 
substance  in  equilibrium  with  its  saturated  solution  is  melted  by 
raising  the  temperature  sufficiently  high,  its  solubility  at  this  tem- 
perature is  the  same  for  the  solid  and  for  the  liquid  state.  This 
is  again  a  necessary  consequence  of  the  principle  that  when  a 
system  is  in  equilibrium  in  one  sense  it  must  be  in  equilibrium  in 
every  sense.  If  the  solid  form  can  exist  in  contact  with  the  liquid 
form  (and  this  is  the  definition  of  the  melting  point),  both  must 
exist  in  contact  with  the  saturated  solution.  This  is,  however, 
only  possible  when  the  solubility  of  the  two  forms  is  the  same  at 
this  temperature,  for  if  the  solubilities  were  different,  similar  con- 
siderations to  those  given  in  Sec.  69  for  vapour  pressure  can  be 
applied,  and  with  their  help  we  could  prove  the  impossibility  of 
the  coexistence  of  the  two  forms. 

Heat  is  always  absorbed  during  melting,  and  therefore  the  heat 
of  solution  of  the  liquid  form  must  differ  from  that  of  the  solid 
form  by  an  amount  equal  to  the  heat  of  melting..  According  to 
the  law  of  the  conservation  of  energy  two  conditions  must  exhibit 

*  The  point  b  does  not  lie  on  the  direct  prolongation  of  the  known  portion 
of  the  solubility  curve.  One  reason  for  this  is  that  saltpetre  undergoes  an 
allotropic  transition  at  129.5°  and  the  appearance  of  the  new  form  therefore 
corresponds  to  a  new  solubility  curve  as  indicated  in  the  figure. 


SOLUTIONS 


159 


the  same  difference  of  energy  whatever  the  way  by  which  the 
system  is  changed  from  the  first  condition  to  the  second.  Imagine 
the  solid  body  first  to  be  dissolved  as  such  at  the  melting  point, 
and  let  its  heat  of  solution  be  s.  Suppose  that  in  the  second  case 
we  melt  the  body  first,  allowing  it  to  absorb  the  heat  of  melting^  /, 
and  then  dissolve  it.  It  will  take  up  the  heat  of  solution  /.  In 
accordance  with  the  principle  just  mentioned  we  will  have  s  =  l+f, 
and  in  this  formula  the  heat  absorbed  by  the  system  is  to  be  called 
positive. 

The  change  of  solubility  with  the  temperature  is  directly  con- 
nected with  the  heat  of  solution,  and  both  are  either  positive  or 
negative.  When  heat  is  absorbed  during  the  process  of  solution 
the  solubility  increases  with  rising  temperature.  If,  therefore, 
the  heat  of  solution  exhibits 
a  sudden  decrease,  as  it 
does  at  the  melting  point, 
where  it  becomes  smaller 
by  the  amount  of  the  heat 
of  melting,  the  increase  of 
solubility  with  the  tem- 
perature must  also  exhibit 
a  sudden  decrease.  This 
means  that  the  solubility 
curve  of  the  liquid  will 
exhibit  a  less  increase  (or 
a  greater  decrease)  for  a 
given  change  of  tempera- 
ture than  that  corresponding  to  the  solid  body.  We  have  already 
found,  however,  .that  the  two  solubilities  must  be  the  same  at 
the  melting  point.  This  means  that  the  solubility  curve  of  the 
liquid  must  connect  with  that  of  the  solid  body  at  the  melting 
point  at  an  angle,  as  is  shown  in  Fig.  19. 

On  the  other  hand,  we  may  suppose  the  liquid  to  be  subcooled, 
arid  the  question  as  to  its  solubility  in  this  condition  is  then  to  be 


CONCENTRA  TION 
FIG.  19. 


160  FUNDAMENTAL   PRINCIPLES  OF  CHEMISTRY 

considered.  This  condition  corresponds  to  a  regular  continuance 
of  the  liquid  state  beyond  the  melting  point,  for  the  melting  point 
is  not  a  singular  point  for  the  liquid,  but  is  characteristic  of 
equilibrium  between  the  liquid  and  the  solid  phase,  and  is  there- 
fore equally  dependent  upon  both  phases.  The  solubility  curve 
of  the  subcooled  liquid  must  therefore  bear  such  relation  to  that 
of  the  solid  body  that  it  indicates  a  greater  solubility  of  the 
solid  body  in  the  subcooled  liquid,  and  in  the  same  way  if  it 
were  possible  to  superheat  the  solid  body  without  melting  it,  its 
solubility  above  the  melting  point  must  be  greater  than  that  of 
the  liquid.  Both  these  facts  are  immediately  evident  from  Fig.  19, 
where  the  regions  of  suspended  transformation  are  indicated  by 
dotted  lines. 

The  general  conclusion  is  that  the  solubility  of  the  less  stable 
form  is  always  greater  than  that  of  the  more  stable  form,  and  this 
same  conclusion  might  have  been  reached  directly  by  reasoning 
similar  to  that  of  Sec.  69,  merely  replacing  vapour  pressure  by 
solubility  in  the  discussion.  The  fact  that  it  is  possible  to  arrive 
at  the  same  conclusion  in  various  ways  is  a  confirmation  of  the 
correct  nature  of  the  reasoning  involved.  Fig.  19  is  fundamentally 
in  agreement  with  Fig.  3  of  Sec.  70,  which  represents  the  relation 
between  vapour  pressures  of  stable  and  unstable  forms.  In  this 
discussion  we  have  made  one  assumption  for  the  sake  of  sim- 
plicity, and  this  assumption  must  be  kept  clearly  in  mind,  because 
it  is  not  always  a  permissible  one.  It  was  that  the  liquid  form  of 
the  dissolved  substance  should  be  present  in  contact  with  the 
solution  without  dissolving  any  of  the  other  substance,  which  we 
have  termed  the  solvent.  This  is  almost  always  true  of  solids,  as 
we  have  already  frequently  stated,  but  in  the  case  of  liquids  it  is 
not  generally  true.  We  must  therefore  inquire  what  changes  are 
introduced  into  our  conclusion  when  this  circumstance  is  taken 
into  account. 

If  the  liquid  form  is  changed  by  dissolving  some  of  the  other 
substance  it  is  no  longer  in  equilibrium  with  the  solid.  We  know 


SOLUTIONS  161 

from  Sec.  117  what  the  nature  of  the  change  in  equilibrium  must 
be.  By  solution  of  a  second  substance  in  the  liquid  phase  the 
equilibrium  temperature  is  always  lowered,  and  the  lowering  is 
proportional  to  the  amount  of  dissolved  substance.  Equilibrium 
between  the  saturated  solution,  the  solid,  and  the  molten  phase 
will  therefore  not  exist  exactly  at  the  melting  point  of  the  solid 
form,  but  will  lie  at  a  lower  temperature,  arid  the  lowering  of  the 
equilibrium  point  will  be  proportional  to  the  solubility  of  the 
solvent  in  the  molten  phase. 

We  have  in  fact  another  case  where  two  liquids,  the  solution 
and  the  molten  phase,  can  only  exist  in  equilibrium  when  each  of 
them  has  become  a  saturated  solution  with  respect  to  the  other. 
We  have  two  constituents  and  three  phases,  two  liquid  phases  and 
the  solid,  and  we  have  therefore  one  degree  of  freedom.  The 
temperature  corresponding  to  equilibrium  is  therefore  variable 
with  pressure.  But  since  none  of 'the  three  phases  is  gaseous, 
pressure  can  have  but  slight  influence  on  the  equilibrium.  The 
remaining  degree  of  freedom  can  be  fixed  by  assuming  a  definite 
pressure,  that  of  one  atmosphere,  for  example.  It  can  also  be  fixed 
by  the  formation  of  a  fourth  phase,  a  vapour  phase,  for  example. 
There  is  then  no  degree  of  freedom,  and  this  means  that  the  vapour 
phase  can  only  exist  in  the  presence  of  the  three  other  phases 
under  definite  conditions  of  temperature  and  pressure. 

121.  THE  SOLUBILITY  OF  ALLOTROPIC  FORMS.  —  Similar  rea- 
soning may  be  used  in  the  discussion  of  the  relation  existing  at 
saturation  between  allotropic  forms  of  the  same  substance.  This 
can  be  immediately  predicted,  for  the  change  from  one  allotropic 
form  to  another  is  fundamentally  in  no  way  different  from  the 
change  from  one  state  to  another,  and  it  is  especially  similar  to 
the  changes  occurring  during  melting  and  solidification.  At  the 
transition  temperature  of  two  allotropic  forms  which  are  in  equi- 
librium their  solubility  must  be  the  same,  and  the  solubility  curves 
of  the  two  forms  will  cut  one  another  at  that  point  at  an  angle. 
On  either  side  of  this  point  that  form  which  is  unstable  in  the 
11 


162  FUNDAMENTAL   PRINCIPLES  OF  CHEMISTRY 

temperature  region  in  question  will  have  the  greater  solubility.* 
In  general  we  can  say  that  the  less  stable  form  will  have  the  greater 
solubility,  and  vice  versa.  But  this  statement  holds  only  for  solu- 
tions of  two  constituents,  and  when  more  are  present  the  relations 
are  much  more  complex. 

This  leads  to  the  question  how  forms  behave  which  are  unstable 
in  the  entire  observable  range  of  conditions,  and  the  answer  is 
that  in  the  whole  region  they  will  be  more  soluble  than  the  stable 
form.  This  affords  a  further  means  of  recognising  mutual  rela- 
tions of  stability  between  allotropic  forms,  even  when  the  proof 
of  actual  transformation  is  impossible  because  of  very  small  re- 
action velocities. 

A  necessary  assumption  in  all  this  is  that  the  solutions  of  the 
various  forms  must  have  exactly  similar  properties  when  their 
concentrations  are  the  same.  If  the  solutions  are  in  any  way 
different,  the  proof  just  given  for  the  transition  of  one  form  into 
the  other,  as  shown  by  the  dissolved  portion,  cannot  be  applied. 
The  substances  in  question  behave  as  any  two  different  substances 
would  which  have  no  definite  relation  to  each  other.  The  reason- 
ing which  leads  to  these  conclusions  is  applicable  for  all  solvents, 
and  it  therefore  follows  that  the  general  relations  are  independent 
of  the  nature  of  the  solvent  just  as  they  are  independent  of  the 
nature  of  the  dissolved  substance.  If  we  are  dealing  with  allo- 
tropic forms  giving  identical  solutions  the  above  considerations 
hold  under  all  circumstances. 

122.  SOLUTIONS  OF  HIGHER  ORDER.  —  These  general  princi- 
ples have  been  applied  to  solutions  of  the  second  order,  that  is,  to 
such  as  can  be  separated  into  or  prepared  from  two  pure  sub- 
stances. There  are,  beside,  solutions  of  higher  order  which  can 
be  separated  into  three,  four,  or  more  constituents,  and  which 
therefore  require  the  same  number  of  pure  substances  for  their 

*  Figure  18  is  in  agreement  with  this.  The  solubility  curve  of  the  new 
form  will  have  a  steeper  slope  than  the  ordinary  solubility  curve,  since  the 
appearance  of  the  new  form  is  accompanied  by  an  increase  of  entropy. 


SOLUTIONS  163 

preparation.  The  special  laws  which  describe  such  solutions 
become  more  and  more  complex  in  the  higher  orders,  but  the 
general  relations  remain  the  same.  It  is  always  possible  to  sepa- 
rate each  of  these  solutions  into  its  constituents,  for  the  concept 
of  solution  depends  upon  the  differences  which  exhibit  them- 
selves when  an  originally  homogeneous  substance  is  subjected 
to  operations  which  result  in  the  formation  and  separation  of 
new  phases. 

123.  THE  GENERAL  PROPERTIES  OF  SINGULAR  POINTS.  — 
Among  solutions  of  higher  order  there  will  be  found  singular 
solutions  which  permit  of  a  change  of  phase  without  any  change 
in  the  properties  or  the  composition  of  the  residue.  As  far  as  such 
a  transformation  is  concerned  they  behave  like  pure  substances.  In 
agreement  with  singular  binary  solutions  they  possess  this  property 
only  at  a  definite  temperature  and  a  corresponding  pressure,  and 
they  lose  it  when  these  are  varied. 

Two  cases  are  to  be  distinguished  among  singular  binary  solu- 
tions. The  solution  may  either  change  into  another  solution,  or 
into  a  mixture  having  the  same  composition  as  the  original  solu- 
tion. The  first  case  corresponds  to  solutions  with  a  constant  boil- 
ing point;  the  second,  to  eutectic  solutions.  The  transformation 
of  two  mutually  saturated  liquid  solutions,  described  in  Sec.  114, 
belongs  to  the  second  case.  These  solutions  boil  at  a  constant 
temperature  and  form  a  vapour  of  constant  composition.  But 
complete  transformation  of  such  a  mixture  into  vapour  under 
constant  conditions  can  only  take  place  when  the  total  composi- 
tion of  the  mixture  is  the  same  as  that  of  the  constant  vapour. 
Of  course  the  liquid  mixture  can  be  primarily  made  up  of  any 
amount  whatever  of  the  two  solutions,  and  it  will  then  boil  at  the 
definite  temperature.  This  will,  however,  only  continue  while 
both  liquid  phases  are  present.  If  one  of  the  phases  boils  away 
before  the  other  under  continued  distillation,  boiling  can  no  longer 
take  place  at  constant  temperature,  and  the  remaining  solution 
will  continue  to  boil  with  a  rising  temperature.  The  transfer- 


164  FUNDAMENTAL  PRINCIPLES  OF  CHEMISTRY 

mation  has  not  taken  place  under  constant  conditions.  It  is 
therefore  necessary  that  both  solutions  should  be  present  in  such 
proportions  that  their  total  composition  is  the  same  as  that  of 
the  vapour,  and  only  under  these  conditions  will  both  solutions 
disappear  at  the  same  time. 

The  ternary  and  higher  solutions  behave  in  a  similar  manner. 
There  are  cases  where  a  solution  evaporates  to  form  a  liquid  of 
the  same  composition.  The  temperature  and  the  pressure  are 
necessarily  constant  during  this  transformation,  for  the  new 
phase  has  the  same  composition  as  the  old  one.  The  composi- 
tion of  the  residue  remains  unchanged,  and  it  therefore  has  a  con- 
stant boiling  point.  This  boiling  point  is  always  a  maximum  or  a 
minimum,  so  that  solutions  which  are  formed  from  the  singular  one 
by  a  slight  change  in  composition  in  either  direction,  all  have  a 
lower  or  a  higher  boiling  point.  If  this  were  not  the  case  the  solu- 
tion would  send  out  vapour  of  such  composition  that  the  residue 
would  have  a  higher  boiling  point  than  the  distillate,  and  if  solu- 
tions with  higher  and  lower  boiling  points  chosen  from  the  imme- 
diate neighbourhood  of  the  singular  solution  are  examined,  they 
will  be  found  to  change  in  composition  during  distillation. 

The  three  singularities,  constant  boiling  point,  constant  com- 
position of  residue  and  distillate,  and  maximum  or  minimum 
boiling  point,  are  therefore  necessarily  connected,  and  each  of  them 
conditions  the  others.  They  are  -called  singular  values  of  the 
properties  of  these  systems,  and  we  may  draw  the  general  con- 
clusion that  these  singular  properties  always  appear  simultaneously 
for  definite  values  of  the  variable  conditions.  This  is  primarily 
true  of  solutions,  but  it  can  also  be  extended  to  include  all  systems 
which  vary  continuously. 

So  far  we  have  been  considering  cases  where  one  phase  changes 
into  one  other  phase.  Precisely  similar  reasoning  can  be  applied 
where  one  phase  changes  into  several  other  phases.  The  case  of 
the  eutectic  solution,  Sec.  118,  is  an  example  of  this.  Here  the 
total  composition  of  the  two  phases  must  be  the  same  as  the  com- 


SOLUTIONS  165 

position  of  the  single  phase  from  which  they  are  formed.  There  are, 
then,  beside  singular  solutions,  singular  mixtures  which  change 
under  constant  conditions  completely  into  a  new  phase.  For 
such  singular  mixtures  the  proportion  of  the  two  phases  at  equi- 
librium can  no  longer  be  arbitrarily  chosen,  as  is  the  case  for 
mixtures  in  general.  The  proportion  at  equilibrium  must  have  a 
definite  value  wrhich  is  determined  by  the  composition  of  the  new 
phase  into  which  they  are  changed.  If  any  other  relation  of  the 
components  of  the  mixture  is  chosen,  one  of  them  will  be  exhausted 
before  the  other  during  transformation,  and  it  would  then  be 
impossible  for  the  whole  process  to  take  place  under  constant 
conditions. 

Among  solutions  of  the  third  or  higher  order  a  new  possibility 
must  be  added  to  those  already  mentioned.  A  singular  mixture 
may  change  into  another  mixture  which  is  also  a  singular  one. 
In  other  words,  it  is  possible  for  m  phases  to  change  into  n  other 
phases  in  such  a  way  that  the  temperature  and  pressure  remain 
constant  during  the  whole  transformation,  (m  and  n  are  whole 
numbers.)  Such  a  constant  transformation  is  only  possible  when 
the  total  composition  of  the  new  phases  exhibits  the  same  propor- 
tional content  of  the  constituents  as  the  original  mixture.  In  other 
words,  the  total  composition  of  the  residue  must  not  vary  at  any 
time  during  the  process,  and  if  this  is  to  hold  the  new  phases  must 
form  with  relations  of  composition  and  amount  such  that  the 
constituents  are  in  the  same  proportions  as  in  the  original  mixture. 
Then  the  temperature  or  the  pressure  corresponding  to  trans- 
formation will  be  a  maximum  or  a  minimum. 


CHAPTER  VI 
ELEMENTS  AND   COMPOUNDS 

124.  HYLOTROPY.  —  The  mode  of  phase  change  in  which  the 
newly  formed  phases  have  at  every  moment  the  same  properties 
arid  the  same  total  composition  as  the  original  system  is  called  a 
hylotropic  transition,  and  the  general  relations  corresponding  to 
it  are  termed  hylotropy.  The  assumption  of  reversibility  in  the 
changes  of  state  so  far  discussed  means  only  that  the  total  com- 
position of  the  original  system  was  like  the  resulting  one  after  the 
transformation  had  taken  place.  A  hylotropic  transformation 
demands  that  the  relation  of  constituents  in  the  old  system  shall 
be  the  same  as  in  the  new  system  at  every  moment  during  the  whole 
process.  This  special  assumption  brings  with  it  the  condition 
that  the  system  shall  have  singular  properties,  and  therefore  that 
a  hylotropic  transformation  can  only  take  place  at  a  maximum 
or  minimum  value  of  pressure  and  temperature. 

The  simplest  case  of  hylotropic  transformation  is  found  in  the 
change  of  state  of  a  pure  substance.  Whenever  a  substance  changes 
its  state,  that  is,  forms  a  new  phase,  at  constant  values  of  pressure 
and  temperature,  it  is  defined  as  a  pure  substance.  Solutions  are 
characterized  by  the  fact  that  they  form  new  phases  only  under 
variable  conditions.  It  is  possible  to  transform  a  solution  into 
vapour  at  constant  temperature,  but  in  order  to  carry  out  this 
process  the  pressure  must  be  continually  decreased  during  vaporiza- 
tion. It  is  also  possible  to  carry  out  the  transformation  at  constant 
pressure,  but  then  the  temperature  must  be  continuously  raised 
during  the  process. 

We  have  just  been  discussing  singular  solutions  and  singular 

166 


ELEMENTS   AND   COMPOUNDS  167 

mixtures,  and  have  found  transformation  under  constant  condi- 
tions to  be  the  rule  among  them.  They  are  therefore  hylo tropic 
just  as  pure  substances  are,  and  we  must  therefore  keep  clearly  in 
mind  how  they  differ  from  pure  substances.  Singular  or  hylotropic 
solutions  and  mixtures  have  this  property  only  at  one  single  defi- 
nite value  of  temperature  and  pressure.  If  transformation  takes 
place  at  any  other  pressure  and  the  corresponding  temperature, 
such  a  solution  or  mixture  no  longer  exhibits  hylotropy.  The 
new  phase  has  a  different  composition  from  the  residue,  exactly  as 
would  be  the  case  with  any  other  solution  or  mixture. 

The  difference  between  singular  solutions  and  mixtures  on  the 
one  hand  and  pure  substances  on  the  other  is  therefore  that  the 
former  are  hylotropic  only  at  one  single  point  among  all  their 
possible  conditions  of  existence,  while  the  latter  are  hylotropic 
within  the  limits  of  a  finite  region.  This  region  may  be  large  or 
small;  in  certain  cases  it  is  so  large  that  it  includes  the  range  of 
all  attainable  conditions.  Important  properties  and  differences 
among  pure  substances  are  dependent  on  this  fact. 

What  is  meant  by  the  statement  that  a  pure  substance  is  only 
hylotropic  between  the  limits  of  a  definite  range  of  temperature 
and  pressure  ?  It  means  that  the  substance  changes  its  proper- 
ties and  composition  during  a  phase  change,  provided  this  change 
takes  place  outside  the  limits  of  this  region.  But  this  latter  set 
of  properties  belongs  to  solutions  and  mixtures.  If  the  region 
within  which  hylotropy  appears  is  called  the  region  of  stability 
of  the  pure  substance  in  question,  we  can  then  say  that  at  the 
limits  of  the  region  of  stability  pure  substances  change  into  solu- 
tions or  mixtures.  Whether  a  solution  or  a  mixture  is  formed 
from  the  pure  substance  at  the  limits  of  this  region  depends  upon 
circumstances.  Gases  always  form  solutions,  and  solutions  will 
therefore  be  usually  formed  at  high  temperatures.  On  the  other 
hand,  when  the  limit  of  stability  lies  at  ordinary  or  low  tempera- 
tures, mixtures  can  appear.  For  reasons  explained  in  Sec.  67 
pressure  can  have  but  small  effect  when  solids  or  liquids  are  in 


168  FUNDAMENTAL  PRINCIPLES   OF  CHEMISTRY 

question.  It  may,  however,  have  a  very  large  effect  among  gases. 
The  actual  proof  of  the  limits  of  stability  may  be  carried  out,  as 
already  explained,  when  we  consider  the  differences  between  mix- 
tures, solutions,  and  pure  substances.  At  high  temperatures  and 
low  pressures,  and  where  we  must  decide  whether  a  gas  is  a  pure 
substance  or  a  solution,  separation  through  a  porous  partition  will 
be  the  usual  means.  It  should,  however,  be  remembered  that  a 
system  which  can  be  proven  to  be  a  mixture  or  a  solution  by  any 
means  whatever  is  characterized  as  such.  All  possible  proof  can 
therefore  be  made  use  of. 

125.  CHEMICAL  PROCESSES  IN  THE  NARROWER  SENSE.  —  It  is 
always  possible  to  separate  a  solution  into  at  least  two  pure  sub- 
stances, and  every  mixture  also  consists  of  at  least  two.  The 
number  of  pure  substances  present  in  a  system,  or  which  can 
possibly  be  produced  from  it,  is  therefore  increased  whenever  the 
limit  of  stability  is  passed.  A  single  pure  substance  changes  at 
this  point  into  at  least  two  other  pure  substances. 

This  is  a  process  which  differs  in  important  details  from  those 
which  we  have  so  far  investigated.  During  a  change  of  state  a 
pure  substance  changes  into  another  pure  substance,  and  during 
the  formation  and  separation  of  solutions  the  number  of  pure 
substances  remains  unchanged.  We  are  now  dealing  with  new 
processes  in  which  the  number  of  pure  substances  changes.  Pro- 
cesses of  this  sort,  where  several  other  pure  substances  are  pro- 
duced from  a  given  set  of  pure  substances,  are  called  chemical 
processes  in  the  narrower  sense.  The  following  cases  are  possible : 
the  number  of  pure  substances  may  increase,  decrease,  or  remain 
the  same  during  the  process.  Processes  of  the  first  sort  are  usually 
called  analytical  processes  or  separations.  Those  of  the  second 
sort  are  called  synthetic  processes  or  combinations.  The  third  sort 
are  called  " double  decompositions"  or  metastases  when  at  least 
two  pure  substances  take  part.  Cases  where  only  one  pure  sub- 
stance takes  part,  changing  into  another,  we  have  already  taken 
up.  These  are  changes  of  state  in  the  broader  sense  of  the  term, 


ELEMENTS  AND   COMPOUNDS  169 

and  they  include  what  has  been  called  polymvrphy.  If  we  apply 
the  law  of  the  conservation  of  weight  to  these  cases  the  following 
rules  may  be  deduced.  If  a  substance  breaks  up  into  two  or  more, 
the  weight  of  each  of  the  new  substances  must  be  less  than  that 
of  the  original  substance,  because  the  sum  of  the  weights  of  the 
new  substances  must  be  equal  to  the  original  weight.  In  general, 
the  old  substance  can  be  prepared  from  the  new  ones.  The  latter 
are  therefore  called  its  constituents.  The  weight  of  each  con- 
stituent must  then  be  smaller  than  that  of  the  substance  of  which 
it  is  a  constituent.  Whenever  a  chemical  process  has  taken  place, 
and  we  find  that  a  newly  formed  substance  weighs  less  than  the 
original  substance,  we  may  be  sure  that  a  decomposition  has  taken 
place,  even  though  we  have  not  seen  or  weighed  the  other  substance 
which  must  have  been  produced. 

126.  ELEMENTS.  —  Of  course  the  constituents  which  have  been 
produced  in  this  way  are  subject  to  further  examination.  It  is 
possible  that  they  may  change  into  mixtures  or  solutions  when 
temperature  and  pressure  are  changed,  or  they  may  not  show 
any  such  effect.  In  the  first  case  the  mixture  or  the  solution  can 
be  separated  into  pure  substances,  and  one  tries  to  transform  these 
again  into  mixtures  or  solutions.  This  can  be  carried  on  until 
we  have  substances  which  cannot  be  transformed  under  any  con- 
ditions into  mixtures  or  solutions.  Such  substances  cannot  be 
decomposed  or  analyzed:  they  are  called  elements,  or  simple 
substances.  Perhaps  a  better  term  than  the  latter  would  be 
undecomposed  substances. 

If  we  remember  that  the  number  of  substances  has  been  con- 
stantly increasing  during  this  series  of  transformations,  at  least 
two  being  produced  from  one  at  every  step,  the  supposition  is  very 
evident  that  the  number  of  elements  ought  to  be  very  much  greater 
than  the  number  of  compounds.  Experience  has,  however,  taught 
us  that  the  opposite  is  true.  We  know  of  more  than  50,000  differ- 
ent compounds,  but  we  know  less  than  80  elements. 

This   apparent   contradiction   disappears   when   we   find    that 


170  FUNDAMENTAL   PRINCIPLES  OF  CHEMISTRY 

various  compounds  do  not  lead  to  wholly  different  elements  when 
they  are  decomposed,  but  that  one  and  the  same  element  can  be 
prepared  from  very  many  compounds.  By  far  the  greater  number 
of  all  known  compounds  contain  one  and  the  same  element,  carbon. 
The  paths  which  lead  from  compounds  to  elements  run  together 
to  a  comparatively  small  number  of  points,  while,  on  the  other 
hand,  they  separate  in  numberless  directions  when  we  start  from 
the  elements  and  pass  to  the  compounds. 

Elements  possess  two  distinct  characteristics.  First,  in  all 
chemical  transformations  which  are  not  hylotropic  and  which 
start  from  an  element,  weight  can  only  increase,  for  all  non- 
hylotropic  transformations  are  transformations  into  chemical 
compounds.  Such  a  change  can  take  place  only  when  other  ele- 
ments combine  with  the  first  one  to  form  compound  substances. 
The  weight  of  the  new  substance  produced  from  the  element 
must  therefore  necessarily  be  greater  than  that  of  the  element 
itself.  It  is  in  fact  equal  to  the  sum  of  the  weights  of  all  the  ele- 
ments which  enter.  The  second  characteristic  is  that  an  element 
possesses  a  region  of  stability  which  reaches  over  the  entire  range 
of  attainable  pressures  and  temperatures.  It  must  be  noted  that 
the  application  of  other  forms  of  energy  than  heat  and  volume 
energy  very  often  leads  to  the  formation  of  new  substances.  Elec- 
trical energy  is  especially  active  in  this  way.  The  concept  of  the 
region  of  stability  must  therefore  be  expanded  to  include  all  the 
forms  of  energy. 

It  must  be  kept  in  mind  that  when  an  element  suffers  a  hylo- 
tropic transformation  the  two  forms  may  form  a  mixture  or  a  solu- 
tion. A  pure  substance  will  then  lose  its  second  characteristic 
and  change  into  a  solution  without  the  occurrence  of  a  chemical 
process  in  the  narrower  sense.  The  concept  of  the  region  of  sta- 
bility must  therefore  be  based  on  chemical  processes  in  the  nar- 
rower sense  and  on  non-hylotropic  transformations.  An  element  is 
a  substance  which  cannot  be  transformed  into  another  non-hylotropic 
substance  within  the  entire  range  of  attainable  energy  influences. 


ELEMENTS  AND  COMPOUNDS  '171 

By  energy  influences  we  must  understand  any  process  which  is 
carried  out  without  the  actual  addition  of  other  substances. 

The  two  definitions  are  knit  together  by  the  law  of  the  conserva- 
tion of  weight,  for  if  a  substance  can  change  into  another  non- 
hylotropic  substance,  this  is  only  possible  if  it  forms  a  mixture  or 
a  solution  of  at  least  binary  composition.  Such  a  system  can 
always  be  separated  into  its  constituents  by  some  means  or  other. 
If  therefore  a  new  hylo tropic  substance  is  produced,  at  least  one 
other  substance  of  the  same  kind  must  be  produced  at  the  same 
time.  Since  the  total  weight  of  the  two  substances  must  be  equal 
to  the  weight  of  the  original  substance,  according  to  the  law  of 
the  conservation  of  weight,  each  of  the  new  substances  must  have 
a  less  weight  than  the  original  substance.  If  this  is  excluded  by 
definition  the  substance  can  only  suffer  hylotropic  transformations 
of  such  a  nature  that  the  weight  does  not  change,  or  chemical 
transformations  with  the  addition  of  other  substances,  and  in  this 
case  the  weight  can  only  increase. 

127.  THE  REVERSIBILITY  OF  CHEMICAL  PROCESSES.  —  So  far 
we  have  regarded  the  chemical  state  of  any  given  system  as  a  de- 
termined function  of  existing  conditions,  especially  pressure  and 
temperature.  By  changes  in  these  conditions  changes  in  the 
system  are  brought  about.  This  assumption  contains  another, 
which  is  that  every  process  is  reversible,  that  is,  that  any  trans- 
formation caused  in  this  way  can  be  reversed  with  the  production 
of  the  original  system.  According  to  the  assumption  already 
made,  it  is  only  necessary  to  arrange  for  the  original  conditions, 
and  especially  for  the  original  values  of  pressure  and  temperature; 
for  if  the  condition  of  the  system  is  only  dependent  on  those  varia- 
bles this  must  result  in  a  return  to  the  original  condition. 

This  assumption  holds  for  the  simple  cases  which  we  have  so 
far  considered.  A  pure  substance  can,  in  general,  be  transformed 
forward  and  backward  into  any  of  its  various  states.  The  ease 
with  which  this  takes  place  may  be,  however,  very  different  in 
different  cases,  and  the  mutual  transformation  of  solid  allotropic 


172  FUNDAMENTAL   PRINCIPLES  OF  CHEMISTRY 

forms  often  takes  place  so  very  slowly  as  to  almost,  and  sometimes 
quite,  pass  the  limits  of  experimental  investigation.  Even  in  these 
cases,  however,  it  is  usually  possible  to  solve  the  problem  by 
roundabout  methods,  so  that  the  law  of  reversibility  appears  to 
be  generally  true  for  these  simple  processes.  The  same  holds  true 
for  the  formation  and  decomposition  of  solutions.  There  is  in 
general  not  the  slightest  difficulty  in  producing  solutions  of  any 
given  constituents,  provided  the  substances  are  capable  of  form- 
ing such  solutions  at  all.  The  separation  of  solutions  into  their 
constituents  is  a  much  more  difficult  and  painstaking  task,  since 
many  methods  of  separation  require  an  unlimited  number  of 
operations.  Even  here,  however,  we  can  feel  sure  of  the  general 
possibility  of  separating  all  solutions  into  their  constituents.  It 
may  be  mentioned  that  the  task  becomes  more  difficult  as  the  order 
of  the  solution  increases.  This  means,  of  course,  that  there  are 
more  constituents  to  separate. 

The  principle  of  the  reversibility  of  chemical  transformations 
is  by  no  means  capable  of  such  general  application  to  chemical 
reactions  in  the  narrower  sense  of  the  word.  The  transformation 
of  compound  pure  substances  into  simpler  ones,  and  finally  into 
elements,  is  theoretically  always  possible,  but  sometimes  practical 
only  by  roundabout  methods.  But  the  preparation  of  substances 
from  simpler  ones,  or  from  the  elements,  is  in  many  cases  im- 
possible at  the  present  time.  In  other  words,  the  analysis  of  a 
substance,  and  especially  the  elementary  analysis  by  which  its  ele- 
ments are  determined,  is  always  possible.  Synthesis,  on  the  other 
hand,  is  not  always  possible,  and  there  are  a  large  number  of  sub- 
stances which  exhibit  transformations  in  one  sense  only  and  which 
cannot  be  produced  from  their  elements. 

Experience  has,  however,  taught  us  something  about  synthesis. 
In  the  earlier  stages  of  the  development  of  chemistry  but  very 
few  syntheses  were  known,  and  chemistry  was  the  art  of  decom- 
posing substances.  The  old  name  "  Scheidekunst"  characterizes 
this  point.  The  progress  of  science  brought  with  it  the  discovery 


ELEMENTS  AND  COMPOUNDS  173 

of  more  and  more  syntheses,  and  at  the  present  time  the  majority 
of  pure  substances  are  not  found  as  such  in  nature,  nor  are  they 
produced  from  natural  products  by  partial  decomposition.  Most 
of  them  are  prepared  in  synthetical  ways.  Certain  substances 
which  are  formed  in  living  plants  and  animals  have  so  far  resisted 
our  attempts  to  prepare  them  synthetically,  but  many  other  sub- 
stances which  are  produced  in  the  same  way  have  already  been 
prepared,  and  there  is  no  real  difference  of  a  fundamental  kind 
between  the  substances  which  are  now  prepared  synthetically 
and  those  whose  synthesis  has  not  yet  been  accomplished.  An 
inductive  conclusion  therefore  seems  scientifically  justified:  the 
boundary  between  substances  which  can  be  synthesized  and 
those  which  cannot  yet  be  prepared  artificially  is  only  set  up  by 
the  conditions  of  our  knowledge  and  skill.  Cases  in  which  a  syn- 
thesis, which  cannot  be  carried  out  at  the  present  time,  will  be- 
come possible  as  the  result  of  scientific  investigation  are  probably 
so  numerous  that  it  seems  only  a  question  of  time  and  labour. 
Sooner  or  later  we  shall  probably  find  a  method  for  the  synthetic 
preparation  of  any  substance  whatever. 

128.  THE  CONSERVATION  OF  THE  ELEMENTS.  —  The  relation 
between  a  compound  and  the  elements  which  can  be  prepared 
from  it,  "  its"  elements,  more  briefly  but  less  correctly,  is  a  fixed 
and  definite  one;  that  is,  given  a  certain  substance,  the  elements 
which  can  be  prepared  from  it  are  determined.  The  method 
which  must  be  used  for  its  decomposition  may  be  one  of  many, 
but  this  fact  has  not  the  slightest  effect  on  the  final  result  of  the 
decomposition ;  that  is,  on  its  elementary  analysis. 

On  the  other  hand,  the  relation  between  the  elements  and  their 
compounds  is  not  a  fixed  and  determined  one.  There  may  be 
several  pure  substances  and  solutions  whose  elementary  analysis 
shows  the  same  elements,  even  though  these  substances  may  possess 
different  properties.  In  the  various  states  (including  allotropic 
solid  forms)  we  have  already  seen  several  examples  of  this.  Those 
substances  which  can  be  transformed  into  one  another,  hylotropic 


174  FUNDAMENTAL   PRINCIPLES  OF  CHEMISTRY 

substances  so  called,  will  always  give  the  same  results  on  ele- 
mentary analysis.  The  method  can  have  no  influence  on  the  re- 
sult, and  we  could  therefore  analyze  the  substance  in  one  case 
directly  and  in  another  case  after  we  have  transformed  it  into  its 
hylotropic  form.  In  both  cases  we  must  obtain  the  same  result. 

Another  expression  for  the  same  fact  may  be  used,  —  it  is  not 
possible  to  transform  one  element  into  another.  This  fact  is  called 
the  law  of  the  conservation  of  the  elements.  If  this  law  did  not 
hold,  elementary  analysis  might  give  different  results  for  the  same 
substance,  one  analysis  being  carried  out  in  such  a  way  as  to  lead 
directly  into  one  set  of  elements,  while  on  another  occasion  these 
might  be  transformed  into  another  set.  From  the  law  of  the  con- 
servation of  the  elements  it  is  also  possible  to  show  that  the  results 
of  elementary  analyses  are  always  definite.  A  difference  in  the 
results  obtained  from  the  same  substance  by  elementary  analysis 
in  different  ways  would  be  equivalent  to  a  transformation  of  the 
elements  produced  in  one  way  into  those  produced  in  another. 

In  so  far  as  the  chemical  processes  in  question  are  reversible, 
the  law  just  given  holds  for  the  synthesis  of  chemical  compounds. 
When  it  is  possible  to  prepare  a  compound  substance  from  its 
elements,  the  same  elements  are  necessary  as  were  found  by  the 
elementary  analysis  of  the  compound.  The  necessity  of  this 
principle  is  contained  also  in  the  law  of  the  conservation  of  the 
elements,  for  if  it  were  possible  in  a  reversible  case  to  prepare  the 
compound  from  elements  other  than  those  obtained  by  its  de- 
composition, it  would  only  be  necessary  to  prepare  the  compound 
from  its  corresponding  elements  and  then  to  decompose  it  into 
other  elements.  The  result  would  be  that  the  first  elements  were 
transformed  into  others. 

129.  SYNTHETIC  PROCESSES.  —  In  order  to  reach  a  general 
idea  of  those  phenomena  which  are  to  be  classified  as  belonging 
to  solutions  and  those  which  belong  to  chemical  reactions  in  the 
narrower  sense,  it  will  be  found  necessary  to  classify  carefully 
the  various  possibilities.  This  is  most  easily  done  if  we  first  fix 


ELEMENTS  AND  COMPOUNDS  175 

the  case  for  solutions  and  then  make  the  assumption  that  when  the 
two  pure  substances  A  and  B  are  brought  together,  forming  the 
new  substance  AB,  this  new  substance  can  form  solutions  with 
both  A  and  B.  In  other  words,  every  type  of  chemical  combina- 
tion can  be  made  by  combining  the  possible  cases  of  solutions, 
pair  by  pair,  until  all  are  exhausted.  One  limitation  must  be  borne 
in  mind.  The  two  types  of  solution  must  have  one  constituent  in 
common  at  the  point  where  they  are  brought  together,  and  this 
is  to  be  the  newly  formed  substance  AB. 

We  can  limit  the  problem  still  further  by  assuming  that  the 
phenomena  of  combination  of  A  and  B  are  observed  at  constant 
temperature  and  pressure.  Out  of  all  the  changes  observable 
under  these  conditions,  such  as  change  of  colour,  of  entropy,  or  the 
heat  condition,  in  general  of  volume  or  of  state,  only  the  latter 
are  to  be  considered.  The  question  is,  then,  what  changes  of  state 
can  take  place  when  we  bring  together  the  two  substances  A  and 
B  in  varying  proportions  ? 

Beginning  with  the  pure  substance^!,  we  will  make  mixtures  of 
0.9  parts  of  A  and  0.1  part  of  B,  0.8  of  A  to  0.2  of  B,  etc.,  to  pure 
B,  observing  any  change  of  state  which  may  take  place  in  any  of 
these  mixtures.  In  certain  cases  it  will  be  desirable  to  choose  the 
steps  closer  together  to  determine  especially  those  proportions  where 
a  new  state  appears  or  an  old  one  vanishes.  Theoretically  every 
possible  proportion  must  be  examined ;  this  is  practically  impos- 
sible, and  it  is  also  unnecessary,  because  of  the  law  of  continuity. 

130.  THE  LAW  OF  CONTINUITY.  —  In  previous  considerations 
we  have  frequently  made  use  of  this  law  without  specifically  stating 
or  naming  it.  It  is  to  such  a  high  degree  a  matter  of  daily  expe- 
rience that  we  usually  assume  its  truth  without  question.  But 
for  its  correct  application  it  is  necessary  to  examine  more  closely 
into  its  meaning  and  range. 

By  continuous  things  we  understand  such  as  exhibit  no  differ- 
ences in  immediately  adjacent  parts.  This  does  not  mean  that 
parts  which  are  far  apart  either  in  space  or  in  time  may  not  be 


176  FUNDAMENTAL   PRINCIPLES  OF  CHEMISTRY 

different.  For  example,  the  colour  of  the  cloudless  sky  is  not  the 
same  at  the  horizon  and  at  the  zenith.  But  immediately  adjacent 
parts  of  the  sky  do  not  differ  from  each  other,  arid  we  are  therefore 
accustomed  to  say  that  the  blue-gray  colour  of  the  horizon  passes 
over  continuously  into  the  deep  blue  of  the  zenith.  A  thing  is  dis- 
continuous when  immediately  adjacent  parts  are  evidently  different. 

The  law  of  continuity  expresses  the  fact  that  those  properties 
of  an  object  or  a  process  which  are  mutually  dependent  are  simul- 
taneously continuous  or  discontinuous.  Discontinuity  is  not  ex- 
cluded, but  the  law  does  say  that  when  any  one  property  becomes 
discontinuous  at  a  certain  point,  all  the  other  properties  which 
are  definitely  connected  with  the  first  one  become  discontinuous 
at  the  same  point.  When  water  freezes,  for  instance,  it  is  not  only 
the  mechanical  properties  which  show  a  sudden  change  when  the 
liquid  changes  to  a  solid;  the  volume,  the  index  of  refraction,  the 
heat  capacity,  and  all  the  other  specific  properties  also  change 
suddenly.  And,  on  the  other  hand,  no  property  of  water  shows 
a  discontinuous  change  when  the  water  is  heated,  compressed,  or 
otherwise  subjected  to  a  continuous  change  of  condition  without 
any  change  in  state. 

Proper  application  of  this  law  demands  that  certain  difficulties 
connected  with  the  definition  of  the  concepts  involved  should  be 
carefully  explained.  The  proof  of  continuity  or  discontinuity  is 
dependent  on  experimental  aid.  A  green  pigment,  produced  by 
mixing  blue  and  yellow,  would  be  continuously  green  as  judged 
by  the  eye  alone.  Under  the  microscope  the  yellow  and  blue 
grains  can  be  seen  side  by  side.  A  coat  of  this  pigment  looks 
smooth  to  the  unaided  eye,  but  the  microscope  would  show  it  to 
be  most  uneven  and  full  of  grains.  In  the  same  way  other  proper- 
ties would  appear  continuous,  as  measured  in  terms  of  a  unit  of 
a  few  tenths  of  a  millimetre,  while  they  become  discontinuous 
when  a  smaller  unit  is  applied.  The  application  of  the  law  demands 
corresponding  caution  whenever  it  is  to  be  used  at  a  boundary  of 
this  kind  between  continuity  and  discontinuity. 


ELEMENTS  AND  COMPOUNDS 


177 


A  still  further  difficulty  is  to  be  found  in  the  concept  of  "  defi- 
nitely connected"  properties.  For  example,  the  vapour  pressure 
of  water  at  0°  is  the  same  as  that  of  ice  at  the  same  temperature, 
in  spite  of  the  fact  that  the  two  states  are  discontinuously  different. 

For  our  own  special  purpose  we  shall  apply  the  law  of  continuity 
in  the  following  way :  When  we  change  the  proportions  of  A  and 
B  step  by  step,  and  no  new  phase  appears  as  we  go  from  one  step 
to  the  next,  we  will  assume  that,  within  the  limits  of  this  step,  no 
discontinuous  change  has  taken  place  in  any  of  the  variable  prop- 
erties. It  is,  of  course,  still  possible  that  within  the  limits  of  this 
step  a  new  phase  has  appeared,  disappearing  again  a  little  later, 
so  that  its  appearance  would  be  overlooked  unless  the  intermediate 
region  were  examined.  This  possibility  diminishes  as  the  steps 
are  chosen  closer  together,  and  can  be  practically  excluded. 

The  most  important  practical  application  of  the  law  of  con- 
tinuity is  in  interpolation.  If  a  number  of  values  of  one  property 
and  the  corresponding  values  of  another  continuously  variable 
property  have  been  determined,  it  can  be  assumed  that  the  values 
lying  between  these  deter- 
mined points  will  follow 
each  other  continuously. 
But  this  does  not  yet  de- 
termine these  intermediate 
points  definitely.  Suppose 
the  two  properties  laid  off  on 
horizontal  and  vertical  axes, 
and  that  1,  1';  2,  2';  3,  3', 
etc.,  are  the  points  deter- 
mined. An  unlimited  num- 
ber of  continuous  lines  can  be 
drawn  through  these  points, 

and   some  of  them  are  indicated  in   Fig.   20.      But    among  all 
these  curves   one  is   the  most  continuous,  and  it  has  less  twists 
than  any  of    the  others.      It  will  be  easily  recognised  from   the 
12 


23 
FIG.  20. 


178  FUNDAMENTAL   PRINCIPLES   OF  CHEMISTRY 

figure,  and  this  is,  in  general,  the  curve  which  actually  repre- 
sents the  relation  in  question.  This  can  always  be  shown 
by  measurement  of  intermediate  points. 

Interpolation  within  the  entire  range  of  measurements  can  be 
carried  out  with  an  accuracy  which  can  be  made  as  great  as  de- 
sired by  the  determination  of  intermediate  points.  This  accuracy 
becomes  less  and  less  as  the  law  of  continuity  is  applied  to  extra- 
polation beyond  the  limits  of  the  measurements.  Points  lying  near 
the  last  measured  one  can  be  fixed  with  considerable  certainty. 
In  Fig.  21  the  assumption  that  X/  is  the  real  point  corresponding 


xt 


X? 

x; 
x; 


FIG.  21. 

to  'Xlt  and  that  X"  and  X"'  are  not,  is  perfectly  justified,  pro- 
vided the  heavy  line  represents  a  set  of  measurements.  But  at 
X2',  X2",  and  X2'"t  corresponding  to  X2,  points  equally  far  apart 
with  XS,  X^',  and  AT/",  no  conclusion  as  to  which  is  the  correct 
point  is  possible,  because  they  all  lie  too  far  from  the  last  measured 
point.  Extrapolation  is  generally  to  be  avoided,  and  in  those 
cases  when  it  is  used  it  must  be  specially  justified.  The  absolute 
temperature  (Sec.  34)  is  determined  by  extrapolation,  and  in  this 
case  its  use  is  certainly  of  value. 


ELEMENTS   AND   COMPOUNDS  179 

131.  GRAPHIC  REPRESENTATION.  —  In  order  to  give  clear  and 
evident  expression  to  the  following  relations  we  will  make  use  of 
diagrammatic  representation. 

The  composition  of  systems  made  up  of  the  two  pure  sub- 
stances A  and  B  will  be  laid  off  along  a  horizontal  line,  the  content 
of  A  decreasing  and  that  of  B  increasing  as  we  pass  from  left  to 
right.  The  left  end  of  the  line  corresponds  to  pure  A,  the  right 
to  pure  B,  and  the  middle  point  represents  a  system  made  up  of 
equal  parts  of  A  and  B.  By  "  parts"  we  may  mean  parts  by 
weight,  but  the  diagram  remains  the  same  for  any  other  method 
of  determining  quantity.  We  could  replace  it  just  as  well  by 
volumes  or  "  combining  weights." 

The  diagrams  are  to  show  what  phases  can  exist  when  pure  A 
and  pure  B  are  brought  together  in  various  proportions,  and  to 
make  this  clear  we  shall  use  heavy  lines  for  solid,  light  lines  for 
liquid,  and  dotted  lines  for  gaseous  phases. 

Pressure  and  temperature  are  assumed  to  remain  constant,  and 
we  have  therefore  disposed  of  two  degrees  of  freedom.  The  phase 
rule  tells  us  that  the  sum  of  phases  and  degrees  of  freedom  for  two 
components  (which  is  the  number  we  are  to  begin  with)  is  always 
four.  Our  system  can  therefore  contain  either  one  phase  or  two. 
Three  or  four  phases  are  only  possible  when  definite  fixed  values 
for  pressure  and  temperature  are  chosen,  such  that  the  substances 
in  question  can  exist  in  three  or  four  phases  in  equilibrium.  For 
our  purpose  these  cases  may  be  omitted  for  the  present,  since  we 
are  not  dealing  with  any  particular  substance.  We  shall  find 
them  again  later  when  we  come  to  the  investigation  of  the  effect 
of  changes  of  pressure  and  temperature  on  such  systems. 

If  only  one  phase  is  present,  one  degree  of  freedom  still  remains ; 
so  wherever  a  single  line  appears  in  a  diagram,  this  means  a  phase 
of  variable  composition  varying  between  the  limits  of  this  region 
of  a  single  phase.  The  line  ab  of  Fig.  22  shows  such  a  case,  and 
this  line  describes  a  liquid  varying  in  composition  between  0.6  of  A 
with  0.4  of  B,  to  0.3  of  A  with  0.7  of  B. 


180  FUNDAMENTAL  PRINCIPLES  OF  CHEMISTRY 

Wherever  two  lines  are  shown  two  phases  are  indicated,  and 
there  remains  no  degree  of  freedom.  Each  of  the  two  phases  has 
therefore  a  constant  composition.  Such  pairs  of  lines  cover  a 
finite  region  only,  and  the  difference  in  total  composition,  indi- 

a b 

L l^_^__t it  |  |  I  I  I  t 

A  as  & 

FIG.  22. 

cated  by  the  extent  of  the  lines,  corresponds  to  a  change  in  the 
amount  of  each  phase  which  is  present.  The  ends  of  such  double 
lines  correspond  to  the  composition  of  one  of  these  constant  phases. 
The  double  line  ab  of  Fig.  23  indicates  that  within  this  region 
a  liquid  phase  is  in  equilibrium  with  a  gaseous  one.  At  the  left, 
where  A  is  present  in  excess,  we  find  a  gaseous  phase  of  variable 
composition.  At  a  a  liquid  phase  appears,  at  first  in  very  small 
amount,  and  the  composition  of  the  gaseous  phase  at  a  is  fixed  by 
the  position  of  this  point.  The  appearance  of  the  second  phase 
determines  the  fact  that  from  this  point  on  the  first  phase  shall 
have  a  constant  composition.  From  a  to  b  the  gaseous  phase  has 


a 


FIG.  23. 

therefore  the  composition  a.  At  b  the  gaseous  phase  disappears. 
The  composition  of  the  liquid  phase  is  therefore  determined  by 
this  point.  This  composition  is  the  same  throughout  the  entire 
liquid  line,  and  even  the  liquid  which  forms  at  a  in  the  presence  of 
the  gas  has  the  same  composition. 

The  lines  are  not  superimposed  in  these  diagrams,  but  are 
placed  side  by  side  for  greater  clearness.  No  difference  is  indi- 
cated by  the  position  of  a  line  above  or  below  another;  either 
case  means  the  same  thing  as  far  as  we  are  concerned. 


ELEMENTS  AND  COMPOUNDS  181 

132.  SOLUTIONS  MADE  UP  OF  PHASES  IN  THE  SAME  STATE.  - 
Let  us  express  the  facts  we  have  already  learned  about  simple 
solutions  (Sections  76-122)  in  this  new  way  by  means  of  a  dia- 
gram, and  first  of  all  let  us  consider  solutions  made  up  of  two 
components  in  the  same  state.  For  the  sake  of  abbreviation  we 
shall  in  future  designate  gaseous  phases  by  g,  liquid  ones  by  /,  and 
solid  ones  by  s. 

In  Fig.  24,  I,  II y  and  III  represent  the  case  of  two  gases.  They 
may  form  solutions  in  all  proportions,  and  in  this  case  the  dia- 
gram is  merely  a  continuous  dotted  line  (/).  Or  the  temperature 


jr          a 


FIG.  24. 

may  lie  above  the  boiling  point  of  one  of  the  components  but 
below  the  boiling  point  of  a  series  of  solutions.  In  this  case  (//) 
the  addition  of  B  to  A  will  result  first  of  all  in  a  gaseous  solution 
which  will  vary  in  composition  up  to  a  certain  point.  At  this 
point  a  liquid  phase,  having  a  boiling  point  which  is  the  tempera- 
ture of  the  experiment,  will  appear.  The  composition  of  the  gas 
phase  is  shown  by  the  point  a  and  that  of  the  liquid  phase  by  b. 
Between  a  and  b  the  liquid  phase  has  increased  at  the  expense  of 
the  gaseous  one,  and  at  b  the  gas  has  entirely  disappeared.  Be- 
tween b  and  c  we  find  a  liquid  phase  only,  and  this  of  variable 
composition,  but  one  which  has  a  boiling  point  always  higher 
than  the  temperature  of  the  experiment.  At  c  the  boiling  point 
of  another  liquid  solution  is  reached,  and  c  indicates  the  composi- 
tion of  this  solution,  while  d  shows  the  composition  of  its  vapour. 
This  liquid  phase  disappears  again  at  d,  and  from  here  to  the  end 


182  FUNDAMENTAL  PRINCIPLES   OF  CHEMISTRY 

of  the  line  (pure  B)  we  find  again  gaseous  solutions  of  varying 
composition. 

The  third  case  is  still  more  complicated.  It  occurs  whenever 
the  liquid  region  in  the  middle  of  the  diagram  is  not  continuous, 
and  when  separation  of  the  solution  into  two  liquid  phases  takes 
place. 

The  conditions  under  which  such  a  case  can  occur  are  not  often 
met  with,  but  for  the  sake  of  completeness  we  must  examine  it 
with  the  others. 

This  exhausts  the  cases  which  can  occur  if  we  assume  that  no 
point  of  inflection  appears  in  the  boiling  point  curves  of  the  binary 
solutions.  Whether  such  a  case  can  actually  be  excluded  or  not 
we  cannot  here  determine,  and  it  can  only  be  said  that  such  a 
thing  has  never  been  observed.  Succeeding  diagrams  are  given 
with  the  same  assumption,  and  it  remains  for  future  experi- 
ment to  discover  what  would  happen  if  the  incorrectness  of  the 
assumption  should  ever  be  proven. 

In  the  case  of  two  liquids  four  different  phase  schemes  are  pos- 
sible, and  these  are  shown  in  Fig.  25.  The  two  liquids  may  be 


Hdc 

m  - 


FIG.  25. 


soluble  in  each  other  in  all  proportions,  and  the  corresponding 
diagram  will  then  contain  a  single  line  (/,  Fig.  25)  like  the  one 


ELEMENTS  AND  COMPOUNDS  183 

for  gases.  Or  the  liquids  may  possess  only  partial  mutual  solu- 
bility, and  in  this  case  the  two  ends  of  the  diagram  will  be  single 
lines  representing  the  series  of  possible  solutions  of  variable  com- 
position. Saturation  will  then  occur  in  both  sides  of  the  diagram, 
and  between  the  two  points  indicating  this  fact  we  must  draw  a 
double  line  to  indicate  that  two  liquid  phases,  each  of  constant 
composition  but  in  varying  proportions,  can  exist  together  in 
equilibrium.  This  is  all  shown  in  II,  Fig.  25.  We  have  still 
to  consider  the  limiting  case  in  which  the  two  solutions  are  not 
measurably  soluble  in  each  other.  For  this  case  the  double  line 
reaches  from  side  to  side  of  the  diagram  as  in  Ila,  Fig.  25.  This 
case  is  actually  not  different  from  the  general  case  of  II. 

In  the  third  case  a  gaseous  solution  appears  between  the  two 
liquid  ones  (///,  Fig.  25).  Such  a  condition  of  things  is  only  to 
be  expected  when  the  two  liquids  are  near  their  boiling  points, 
and  when  some  of  the  possible  solutions  have  boiling  points  which 
lie  above  the  temperature  of  the  experiment.  At  a  definite  point 
of  composition  vapour  will  then  begin  to  form,  and  its  escape 
leaves  a  residue  which  is  less  volatile,  so  that  it  ceases  to  boil.  We 
have  then  a  region  of  two  phases,  vapour  and  liquid,  and  both 
have  constant  composition.  Finally  a  point  is  reached  where  the 
total  composition  is  the  same  as  that  of  the  vapour,  and  at  this 
point  the  liquid  phase  disappears.  The  vapour  phase  can  now 
change  in  composition  until  a  liquid  phase  separates  again,  and 
the  phenomena  just  described  will  then  appear  in  reverse  order. 

The  fourth  case  IV  will  be  seen  to  be  a  combination  of  cases 
//  and  ///,  and  therefore  needs  no  further  explanation. 

133.  Two  SOLIDS.  —  Two  solids  give  not  less  than  ten  different 
phase  combinations.  As  long  as  no  phase  belonging  to  another 
state  appears,  only  one  case  is  possible  (7,  Fig.  26),  provided  we 
assume  as  usual  that  solid  solutions  are  to  be  left  out  of  considera- 
tion. This  diagram  shows  the  two  solid  phases  existing  together 
through  the  whole  range  without  any  mutual  effect.  But  when 
liquid  and  vapour,  or  both,  occur  between  the  two  ends  of  the  dia- 


184  FUNDAMENTAL   PRINCIPLES  OF  CHEMISTRY 

gram,  a  corresponding  complexity  appears.  Let  us  first  assume 
that  both  solids  vaporize  without  previously  melting.  Let  us 
assume  that  the  temperature  is  lower  than  the  boiling  point  of 
either  substance  (as  we  have  already  assumed  in  saying  that  they 
are  solids),  and  that  the  sum  of  their  two  vapour  pressures  at  the 


m 


VI 


FIG.  26. 


temperature  of  the  experiment  is  greater  than  the  constant  pres- 
sure at  which  the  experiment  is  made.  Then  the  addition  of  B 
to  A  will  soon  cause  the  appearance  of  a  vapour  phase  containing 
all  the  B  so  added  and  as  much  of  A  as  corresponds  to  its  vapour 
pressure.  We  have  then  solid  A  and  a  gaseous  solution  of  A  and  B. 


ELEMENTS  AND   COMPOUNDS  185 

The  addition  of  more  B  results  in  an  increase  in  the  amount  of 
the  vapour  phase  although  the  total  composition  remains  un- 
changed. This  can  only  be  true  when  A  evaporates  in  amount 
proportional  to  the  added  B,  and  it  can  be  carried  on  until  all  of 
A  has  evaporated.  From  this  point  on  the  composition  of  the  gas 
solution  changes  until  B  is  present  in  excess,  and  appears  as  a 
solid  phase  with  the  vapour.  The  vapour  has  from  this  point  a 
constant  composition,  but  decreases  in  proportion  to  B,  until 
finally,  at  the  end  of  the  diagram,  only  pure  B  is  present.  II  ex- 
hibits these  phenomena  in  their  entirety. 

A  precisely  similar  diagram  corresponds  to  the  appearance  of  a 
liquid  phase  in  place  of  the  gaseous  one.  The  condition  for  this 
is  that  the  temperature  shall  lie  below  the  melting  points  of  the 
constituents,  but  above  the  eutectic  point.  The  first  addition  of 
B  to  solid  A  results  in  the  formation  of  a  saturated  liquid  solution 
in  the  presence  of  an  excess  of  A,  and  further  additions  increase 
the  liquid  portion  with  a  corresponding  decrease  in  the  solid  phase. 
Solid  A  finally  disappears  and  the  liquid  phase  begins  to  change  in 
composition  and  continues  until  it  is  saturated  with  solid  B,  when 
this  appears  as  a  solid  phase  in  contact  with  the  solution,  which  has 
remained  constant.  From  this  point  on  the  liquid  phase  decreases 
and  the  solid  phase  increases  until  we  arrive  at  pure  solid  B. 
Diagram  F,  which  corresponds  to  this  set  of  changes,  differs  from 
II  only  in  that  the  dotted  gas  line  is  replaced  by  the  continuous 
liquid  line. 

These  two  simple  forms  become  more  complex  when  the  more 
complicated  gg  lines  can  appear  (as  in  Fig.  24,  II  and  ///)  in 
place  of  the  simple  gas  line  lying  between  the  regions  containing 
two  phases.  Figure  26,  ///  and  IV,  illustrates  this,  and  in  place 
of  the  simple  liquid  line  of  V  we  may  have  the  more  complicated 
lines  //  to  IV  of  Fig.  25.  These  cases  are  shown  in  VI  to  VIII, 
Fig.  26.  It  is  finally  possible  that  vapor  shall  be  present  on  one 
side  of  the  diagram  and  liquid  on  the  other  in  contact  with  the 
solid  phase.  This  is  shown  in  the  cases  IX  and  X.  In  other  words, 


186  FUNDAMENTAL   PRINCIPLES  OF  CHEMISTRY 

diagrams  like  //,  ///,  and  IV  are  produced  when  a  short  thick 
line  is  added  at  each  end  to  the  gg  diagrams  of  Fig.  24  correspond- 
ing to  the  assumption  that  here  a  solid  phase  is  present  with  the 
gas;  and  in  the  same  way  V  to  VIII  are  formed  by  the  same 
process  from  the  //  diagrams  of  Fig.  25.  The  two  last  diagrams 
IX  and  X  are  produced  from  the  diagrams  of  Fig.  27  in  the 
same  way.  This  method  of  examining  the  cases  insures  that  we 
shall  not  miss  any  possible  combination. 

134.  SOLUTIONS   OF   DISSIMILAR   STATES.  —  Beside   the   three 
cases,  gg,  II,  and  ss,  in  which  constituents  in  the  same  state  form 
solutions,  we  have  also  the  three  cases  gl,  gs,  and  Is,  representing 
solutions  made  up  of  constituents  differing  in  state.    In  the  latter 
case  the  symmetry  which  was  observed  in  the  former  case  naturally 
disappears. 

135.  ONE  GAS  AND  ONE  LIQUID.  —  Starting  from  the  gas  side 
we  have  first  of  all  gaseous  solutions  to  the  point  which  represents 
the  vapour  pressure  of  the  liquid.    From  this  point  on  liquid  satu- 
rated with  gas  appears  as  a  second  phase,  and  this  increases  at  the 
expense  of  the  first  phase  until  finally  all  the  gas  disappears.    The 


JL 


FIG.  27. 

end  of  the  series  is  made  up  of  liquid  solutions  of  varying  com- 
position ending  in  pure  E.  This  simplest  case  is  shown  in  /  of 
Fig.  27.  The  second  more  complicated  case  starts  in  exactly  the 
same  way,  but  within  the  region  of  liquid  two  liquid  phases  appear. 
In  other  words,  we  find  a  combination  of  /  and  //,  Fig.  25. 

When  a  gas  reacts  with  a  solid  substance  the  simplest  case  is 
•that  shown  in  I  of  Fig.  28.  Here  the  solid  substance  vaporizes 
until  its  vapour  pressure  at  the  temperature  of  the  experiment  has 
been  reached.  From  this  point  the  liquid  phase  exists  in  the  pres- 


ELEMENTS  AND  COMPOUNDS  187 

ence  of  the  gaseous  phase  to  the  end  of  the  diagram,  because  solid 
substances  do  not  form  solutions  with  gases. 

This  simple  diagram  may  be  complicated  in  many  ways.     A 
liquid  may  appear  before  the  gas  is  saturated  (77).     This  liquid 


n 


FIG.  28. 

may  previously  form  two  phases  (777),  or  it  may  change  into  a 
gaseous  phase  before  the  solid  appears  (IV);  or  a  second  liquid 
phase  may  appear  between  these  two  conditions.  This  exhausts 
the  possibilities. 

Somewhat  similar  to  these  are  the  conditions  which  may  develop 
between  a  liquid  and  a  solid,  and  Fig.  29  represents  the  corre- 
sponding set  of  phases.  Because  of  the  fact  that  two  phases  are 
possible  for  a  liquid,  but  not  for  a  gas,  we  have  one  additional 
case,  so  that  in  toto  six  different  phenomena  may  take  place.  A 
description  of  these  is  unnecessary,  for  no  important  new  relations 
appear. 

An  inclusive  examination  of  the  thirty  cases  just  described  will 
show  that  characteristic  diagrams  appear  when  a  solid  substance 
is  concerned  in  the  process.  Under  these  conditions  the  region  of 
two  phases  runs  in  every  case  to  the  end  of  the  diagram  at  the  side 
representing  the  solid  substance.  In  the  case  ss,  where  two  solids 
are  present,  we  find  double  lines  at  each  end.  This  is  the  natural 


188  FUNDAMENTAL   PRINCIPLES   OF   CHEMISTRY 

expression  for  the  general  assumption  that  solid  substances  do  not 
form  solutions,  for  II  a  of  Fig.  25,  where  a  similar  assumption  has 
been  made,  shows  a  similar  double  line  reaching  to  the  end  of  the 


ST. 


IV- 


vr- 


FIG.  29. 

diagram.  It  may  be  mentioned  that  the  complexity  is  least  among 
gases,  and  that  it  increases  among  liquids,  becoming  greatest  for 
solids. 

136.  THE  TEMPERATURE  Axis.  —  The  considerations  just 
given  become  in  many  respects  more  connected  and  evident  if  we 
do  not  limit  ourselves  to  a  single  temperature.  Both  temperature 
and  pressure  have  been  assumed  to  be  constant,  and  we  had  there- 
fore to  decide  beforehand  which  of  the  two  possible  degrees  of 
freedom  we  would  assume.  Pressure  has  a  very  marked  influence 
on  gases,  but  a  very  slight  one  on  liquids  and  solids,  and  therefore 
the  freedom  of  pressure  would  bring  with  it  for  liquids  and  solids 
no  important  change  in  the  relations  already  given.  On  the  other 
hand,  the  effect  of  temperature  is  present  in  a  marked  degree  for 
all  three  states,  and  a  much  more  complete  representation  is  ob- 
tained when  the  temperature  is  varied.  Representations  of  the 


ELEMENTS   AND   COMPOUNDS  189 

total  effect  resulting  from  change  of  both  pressure  and  tempera- 
ture, together  with  the  change  in  composition,  would  require  three 
variables.  This  means  a  diagram  in  three  dimensions  which  is 
difficult  of  representation,  although  it  is  actually  the  most  complete. 
We  will  therefore  continue  to  represent  composition  along  a  hori- 
zontal line  whose  length  is  unity,  and  we  will  measure  temperature 
in  a  direction  perpendicular  to  this  line.  Each  point  in  any  of  our 
previous  diagrams  is  then  transformed  into  a  line  and  each  line 
into  a  surface.  As  temperature  is  changed,  any  given  point  cor- 
responding to  the  appearance  of  a  new  phase  does  not  remain  in 
its  original  position  along  the  axis  of  compositions,  and  the  lines 
will  therefore,  in  general,  possess  curvature.  They  will  be  con- 
tinuous when  they  represent  continuous  changes  of  the  system,  and 
discontinuous  when  they  represent  discontinuous  changes. 

The  surfaces  which  are  bounded  by  lines  of  this  sort  are  of  two 
kinds,  corresponding  to  two  kinds  of  lines,  single  and  double  ones. 
Surfaces  corresponding  to  one  phase  will  be  developed  by  the  single 
lines,  and  surfaces  corresponding  to  two  phases  by  the  double 
lines.  Just  as  double  lines  are  produced  when  neighbouring 
phases  extend  past  one  another,  so  these  surfaces  of  two  phases  are 
seen  to  be  produced  by  the  superposition  of  two  neighbouring 
surfaces  each  corresponding  to  a  single  phase. 

Horizontal  lines  drawn  through  such  a  diagram  give  phase  dia- 
grams similar  to  those  already  explained,  corresponding  to  a  defi- 
nite temperature  and  to  whatever  pressure  is  assumed  for  the  whole 
diagram.  Vertical  lines  express  a  series  of  conditions  belonging 
to  a  system  of  constant  composition  and  constant  pressure  but 
varying  temperature.  They  correspond  therefore  to  our  ordinary 
laboratory  experiments  in  open  vessels  placed  over  a  flame,  since 
in  this  case  the  temperature  changes  while  pressure  and  composition 
remain  the  same. 

At  high  temperatures  all  substances  change  into  the  gaseous 
state  and  at  low  temperatures  into  the  solid.  Our  diagrams  will 
therefore  have  the  gaseous  state,  in  general,  in  the  upper  part  and 


100  FUNDAMENTAL   PRINCIPLES   OF   CHEMISTRY 

the  solid  state  in  the  lower  part,  with  liquid  conditions  lying  be- 
tween. Each  line  which  separates  the  condition  of  a  gas  from 
that  of  a  liquid  is  a  boiling  point  curve,  for  it  represents  the  tem- 
perature at  which  the  corresponding  systems  boil.  Each  line  which 
separates  a  solid  region  from  a  liquid  one  is  a  melting  point  curve, 
for  it  represents  the  temperature  at  which  the  liquid  and  solid 
phases  can  exist  together.  Finally,  those  comparatively  rare  lines 
which  separate  gaseous  from  solid  substances,  and  which  therefore 
represent  the  transition  of  a  solid  into  a  gaseous  state,  and  vice 
versa,  we  will  call  sublimation  curves,  since  sublimation  has  been 
defined  as  the  vaporization  of  a  solid  without  the  appearance  of 
a  liquid  phase.  The  melting  point  is  only  slightly  affected  by 
pressure,  the  boiling  point  and  sublimation  point  are  affected  very 
strongly.  It  is  therefore,  in  general,  possible  to  make  the  vapori- 
zation point  approach  the  melting  point,  and  sometimes  even  to 
pass  it  by  decreasing  the  pressure.  At  low  pressures  phenomena 
of  sublimation  will  therefore  be  more  common  than  at  high  pres- 
sures. Even  at  atmospheric  pressure  they  are  comparatively  rare. 

137.  BOILING  POINT  CURVES.  —  The  general  course  of  the 
boiling  point  curves  for  binary  solutions  has  already  been  shown 
in  Sec.  106.  We  shall  therefore  consider  the  three  types  with 
special  regard  to  their  possible  phase  diagrams  at  constant  tem- 
perature, that  is,  their  isothermal  phase  diagrams. 

A  boiling  point  curve  without  a  singular  point  is  like  all  similar 
curves.  It  is  a  double  line,  one  branch  of  which  corresponds  to 
the  composition  of  the  liquid,  the  other  to  that  of  the  gas  phase, 
as  in  Fig.  30.  Between  these  two  lines  lies  a  region  common  to 
two  phases,  gas  and  liquid.  The  double  line  therefore  divides 
the  whole  field  into  the  gas  region  g  above,  the  liquid  region  / 
below,  and  these  two  are  superimposed  between  the  double  line  to 
form  the  region  of  two  phases  gl.  In  this  and  in  following  dia- 
grams the  regions  will  be  indicated  by  these  letters. 

If  we  draw  horizontal  lines  at  various  levels  through  the  diagram, 
the  line  marked  1  will  be  found  to  lie  entirely  in  the  gas  region. 


ELEMENTS  AND  COMPOUNDS 


191 


On  the  other  hand,  line  2  cuts  all  three  regions  and  gives  us  a 
phase  diagram  gl  I.  In  the  region  /  we  find  again  the  simple 
liquid  diagram  //  /. 

In  the  case  of  a  boiling  point  curve  with  a  maximum  such  as 
Fig.  31,  we  find  the  gas  line  1  above.  Then  at  2  we  find  the  liquid 
between  two  gaseous  regions  with  regions  of  two  phases  between. 
This  is  the  case  gg  II.  The  line  at  3  gives  us  the  diagram  gly 


FIG.  30. 

and  4  is  a  simple  liquid  line.  In  the  case  of  the  boiling  point  curve 
with  a  minimum,  as  shown  in  Fig.  32,  we  find  first  of  all  a  charac- 
teristic section  2  corresponding  to  gl  I  and  another  3  correspond- 
ing to  the  diagram  //  777.  This  exhausts  all  the  cases  in  which 
gases  appear  with  simple  liquid  phases. 

138.   Two  LIQUID  PHASES.  —  The  formation  of  liquid  double 
phases  is  brought  about  by  the  superposition  of  two  liquid  solu- 


192 


FUNDAMENTAL   PRINCIPLES   OF  CHEMISTRY 


tions,  the  one  containing  more  A  and  the  other  more  B.  The 
region  of  two  phases  therefore  becomes  a  nearly  vertical  band  in 
the  middle  of  the  diagram.  This  band  may  end  in  a  critical  point 
at  higher  temperatures  and  occasionally  at  lower  temperatures. 
Fig.  33  represents  the  first  case.  Above  the  band  we  have  at  1  a 
continuous  liquid  line.  At  2  we  have  the  phase  diagram  //  II.  As 
the  solubility  becomes  less  because  of  lower  temperature  the  band 


FIG.  31. 

extends  itself  to  the  boundaries  at  the  ends,  and  we  have  at  3  the 
double  line  corresponding  to  the  insoluble  pair  of  liquids  //  II  a. 

This  exhausts  the  system  made  up  of  liquid  phases,  for  if  the 
band  is  closed  below,  the  same  set  of  phase  diagrams  is  produced, 
reversed  in  their  order. 

139.  ONE  GAS  PHASE  AND  Two  LIQUID  PHASES.  —  Phase 
diagrams  containing  systems  of  this  kind  are  produced  when  the 


ELEMENTS  AND   COMPOUNDS 


103 


FIG.  32. 


II 


13 


FIG.  33. 


194 


FUNDAMENTAL  PRINCIPLES  OF  CHEMISTRY 


bands  of  the  boiling  point  curves,  or  the  regions  of  existence  of  two 
liquid  phases,  appear  side  by  side  at  the  same  height,  that  is,  at 
the  same  temperature.  All  the  three  forms  of  the  boiling  point 
curve  are  therefore  to  be  combined  with  such  a  region  of  two 
liquids,  and  it  makes  no  special  difference  whether  these  forms 
cut  one  another  or  not.  The  boiling  point  curve  can  be  displaced 


FIG.  34. 

to  a  very  large  extent  by  a  change  in  pressure,  while  the  liquid 
line  remains  practically  unchanged.  It  is  therefore  in  our  power 
to  cause  the  two  regions  to  superimpose  or  separate.  The  con- 
clusion is  evident  that  those  compositions  which  would  give  rise 
to  contradictions  if  they  crossed  one  another  in  the'  diagram  can- 
not be  expected  to  actually  occur,  and  they  may  therefore  be  ex- 
cluded in  further  considerations  as  physically  impossible. 


ELEMENTS  AND  COMPOUNDS  195 

First  let  us  consider  the  combination  of  a  rising  boiling  point 
curve  with  a  region  of  two  liquids,  as  in  Fig.  34.  Only  the  charac- 
teristic section  is  shown  in  the  diagram,  and  this  is  one  which  is 
different  from  any  previous  diagram.  The  case  gl  II  will  be  rec- 
ognised and  all  the  other  sections  result  in  cases  already  examined ; 
these,  therefore,  need  not  be  considered  further.  When  a  con- 


FIG.  35. 

vex  boiling  point  curve  is  combined  with  a  region  of  two  liquids, 
as  shown  in  Fig.  35,  no  new  phase  diagram  results,  and  this  holds 
whether  the  two  regions  cut  one  another  or  not;  but  the  special 
case  shown  in  Fig.  36  gives  a  new  phase  diagram  //  IV.  A  further 
possibility  is  shown  in  Fig.  37,  and  a  form  similar  to  this  might 
be  imagined.  From  previous  considerations  (Sec.  113),  concerning 


196 


FUNDAMENTAL   PRINCIPLES   OF   CHEMISTRY 


the  possible  shape  of  interrupted  boiling  point  curves,  it  will  be 
seen  that  such  a  combination  is  not  to  be  expected  since  a  corre- 
sponding penetration  is  impossible.  The  case  Fig.  38  is  a  possible 
one.  The  characteristic  section  is  the  same  in  both  cases,  as  closer 
examination  will  show. 

140.  THE  MELTING  POINT  CURVE.  —  The  general  course  of  a 
regular  melting  point  curve  has  already  been  explained  in  Sec. 
117.  It  is  applicable  whenever  the  two  substances  are  soluble  in 


FIG.  36. 

all  proportions  in  the  liquid  state,  but  not  at  all  soluble  in  the 
solid  state.  The  curve  is  made  up  of  the  two  nearly  straight 
branches  running  down  toward  the  middle  of  the  diagram  and 
cutting  each  other  at  a  lowest  point  at  the  eutectic  temperature 
(see  Fig.  39). 

In  analogy  with  the  boiling  point  curve  we  may  expect  this  to 
be  a  double  line,  and  if  so,  where  is  the  other  branch  ?  So  far,  all 
the  lines  we  have  drawn  have  been  based  on  the  composition  of 


ELEMENTS   AND   COMPOUNDS 


197 


the  liquid  phase.    Now  we  must  also  include  the  solid  one.    The 

solid  phase  at  one  end  of  the  diagram  consists  of  pure  A ,  and  at  the 

other  end  of  pure  B.    The  other  branch  of  the  curve  is  therefore 

made   up   of   the    two 

vertical     lines     which 

bound     the     diagram. 

They    run    from     the 

melting    point    of    the 

pure  substance  in  each 

case  downward  to  the 

eu  tec  tic  temperature. 

The  left-hand  verti- 
cal corresponds  to  the 
left  portion  of  the 
melting  point  curve, 
and  the  right  to  the 
right  portion.  At  the 
eutectic  point  both 

solid  substances  can  exist  in  equilibrium  with  the  molten  mixture 
or  the  liquid  solution. 

We  have  before  us  a  diagram  similar  to  the  boiling  point  curve 
of  Fig.  32,  with  one  difference.  Here  one  branch  of  the  double 
line  lies  at  the  very  edge  of  the  diagram,  and  it  is  made  up  of  two 
separate  pieces. 

If  horizontal  (isothermal)  lines  are  drawn  through  the  diagram 
at  various  heights  we  obtain  the  following  cases :  at  1  the  simple 
line  for  a  liquid;  at  2  the  system  ls\  at  3  sis;  and  at  the  bottom  of 
the  diagram,  below  the  eutectic  temperature,  ss.  As  is  evident, 
equilibrium  with  solid  phases  is  indicated  by  the  fact  that  the 
regions  of  two  phases  extend  left  and  right  to  the  edge  of  the  dia- 
gram. Among  liquids  and  gases  variable  solutions  (regions  of  a 
single  phase)  generally  appear  at  the  edges  of  the  diagram. 

There  is  no  other  type  of  melting  point  curve,  and  so  the  possible 
cases  of  equilibrium  between  solid  and  simple  liquid  phases  are 


FIG.  37. 


198  FUNDAMENTAL   PRINCIPLES   OF  CHEMISTRY 


FIG.  38. 


FIG.  39. 


ELEMENTS  AND  COMPOUNDS  199 

exhausted.  More  complicated  cases  in  which  two  liquid  phases 
are  present  will  be  taken  up  a  little  later. 

141.  THE  SUBLIMATION  CURVE.  —  Solid  substances  do  not 
usually  form  solutions  with  gases  any  more  than  with  liquids, 
and  we  may  therefore  expect  the  sublimination  curve  for  two 
solid  substances  to  show  the  same  peculiarities  as  those  of  the 
melting  point  curve.  The  relations  are,  in  fact,  still  more  simple 
than  in  the  latter  case,  for  the  gas  laws  are  always  applicable. 

For  each  solid  A  there  will  be  a  temperature  at  which  the  vapour 
pressure  will  equal  the  pressure  under  which  the  experiment  is 
made.  This  temperature  we  may  call  its  boiling  point.  If  some 
of  B  is  added  to  A  it  will  vaporize  and  assume  a  part  of  the  pres- 
sure in  the  gaseous  phase.  The  partial  pressure  of  A  will  then  be 
decreased  and  the  temperature  must  be  lowered  if  the  total  pressure 
is  to  remain  the  experimental  pressure.  The  larger  the  content  of 
B  the  lower  the  partial  pressure  of  A  will  become,  and  this  will 
only  end  when  B  is  completely  vaporized.  Finally,  a  tempera- 
ture will  be  reached  at  which  the  sum  of  the  vapour  pressures  of 
the  two  solids  equals  the  experimental  pressure.  At  this  point 
both  solids  can  exist  in  the  presence  of  the  gaseous  solution  of  their 
vapours,  and  this  is,  moreover,  the  lowest  temperature  at  which 
a  vapour  phase  can  appear  in  the  system.  This  temperature  is 
evidently  analogous  to  the  eutectic  point,  and  the  same  reasoning 
holds  when  we  begin  with  pure  B. 

The  representation  of  these  relations  must  therefore  exhibit  a 
form  precisely  similar  to  the  melting  point  curve.  In  Fig.  17  a 
and  b  are  the  boiling  points  of  the  two  solids  and  e  is  the  "  eutectic 
boiling  point."  As  in  the  previous  case,  the  second  branch  of  the 
curve  is  made  up  of  the  two  vertical  boundaries  of  the  diagram. 
And  in  the  same  way  we  can  obtain  from  Fig.  39  a  corresponding 
set  of  phase  diagrams :  1  is  gg  7,  2  is  gs,  3  is  sgs,  and  4  is  ss,  the 
gas  line  replacing  the  liquid  line  in  each  case.  Even  the  peculiarity 
that  the  single  phase  regions  extend  to  the  edges  of  the  diagrams 
at  each  side  is  also  found  here. 


200  FUNDAMENTAL   PRINCIPLES  OF  CHEMISTRY 

142.  MORE  COMPLICATED  CASES.  —  We  have  now  a  general 
idea  of  the  effect  of  the  appearance  of  new  phases  on  the  systems 
of  liquids  and  gases  already  considered.     Solid  phases  always 
appear  at  the  two  ends  of  the  diagram,  coming  in  from  outside. 
It  will  only  be  found  necessary  to  run  in  solid  phases  at  the  two 
boundaries  at  right  and  left  in  the  earlier  diagrams  in  order  to 
exhaust  all  the  possibilities.     Such  diagrams  can  become  very 
complex  indeed  when  various  phases  are  formed  and  intermingle 
at  various  temperatures,  and  for  our  purposes  we  shall  not  need 
to  follow  them  further.     For  isothermal  conditions  the  intermix- 
ture of  phases  can  only  lead  to  simplification  of  the  diagrams 
already  discussed,  under  the  assumption  that  the  regions  remain 
separated. 

If  the  rules  we  have  used  are  applied  to  various  phase  diagrams, 
it  will  be  found  that  the  symmetrical  ones  (those  in  which  the  two 
substances  are  in  the  same  state)  are  precisely  similar  whether 
the  solid  appears  at  the  right  hand  or  at  the  left.  If  the  two  sub- 
stances are  in  different  states,  different  diagrams  result,  and  the 
two  Is  diagrams  become  four  in  number  when  another  solid  phase 
appears. 

If  these  combinations  are  examined,  it  is  found  that  all  the 
diagrams  previously  considered  from  another  view-point  appear 
again.  This  formal  method  of  exhausting  all  possibilities  by  ar- 
ranging systems  in  various  ways,  examining  them  from  different 
points  of  view,  and  then  comparing  the  independent  variables, 
is  of  great  importance.  It  is,  in  fact,  the  only  way  to  be  sure  that 
no  possible  groups  have  been  overlooked. 

143.  THE   APPEARANCE   OF    CHEMICAL   COMPOUNDS.  —  After 
these  preliminaries  we  are  in  a  position  to  consider  an  important 
question.     When  two  pure  substances  are  brought  together,  will 
a  chemical  compound  be  formed  beside  the  possible  set  of  solutions 
which  may  be  produced  from  them  ?    The  characteristic  of  a  chem- 
ical compound  will  be  that  when  A  and  B  are  brought  together 
in  all  proportions  phase  diagrams  will  be  produced  which  are 


ELEMENTS  AND   COMPOUNDS  201 

different  from  any  of  those  which  describe  mere  solutions.  Such 
diagrams  are  of  frequent  occurrence.  They  therefore  demand  a 
new  discussion  of  the  phenomena  involved,  and  the  assumption 
that  a  new  substance  AB  has  resulted  from  the  interaction  of  the 
two  substances  A  and  B  will  be  found  an  important  aid  in  the 
description  and  representation  of  these  new  phenomena. 

After  experimental  determination  of  the  facts  we  might  prove 
from  the  structure  of  new  diagrams  that  they  lead  to  the  assump- 
tion of  a  new  substance.  We  will  however  assume  it  proven  that 
such  an  assumption  is  practically  applicable.  We  will  examine 
the  consequences  which  can  be  drawn  from  this  assumption.  This 
is  not  only  the  more  convenient  process  of  the  two,  it  also  corre- 
sponds more  nearly  to  the  historical  development  of  the  matter; 
for  long  before  the  development  of  the  phase  rule  it  had  been 
shown  by  experiments  of  another  sort,  especially  by  the  separation 
of  substances  in  pure  form,  that  new  substances  do  appear  under 
these  circumstances.  In  the  course  of  discussion  it  will  be  shown 
that  this  process  can  be  carried  out  and  described  by  means  of 
phase  diagrams,  if  this  is  done  systematically.  For  the  first  part 
of  our  discussion  we  shall  assume  constant  pressure  and  constant 
temperature  for  the  sake  of  clearness,  but  later  all  such  limitations 
must  be  set  aside. 

We  shall  proceed  as  follows :  Let  us  assume  that  two  substances, 
A  and  B,  are  present  in  definite  conditions  of  state.  There  are 
six  possible  cases,  and  these  are  gg,  II,  ss,  gl,  gs,  and  Is.  Any  one 
of  these  pairs  can  give  rise  to  a  new  gaseous,  liquid,  or  solid  sub- 
stance, so  that  eighteen  cases  are  possible.  Each  pair  of  sub- 
stances in  a  definite  state  can  also  give  rise  to  from  two  to  ten 
different  solutions,  and  all  of  these  combinations  must  be  com- 
bined with  each  other.  The  number  of  phase  diagrams  to  be  in- 
vestigated is  therefore  a  large  one.  There  are  366  such  diagrams 
in  all.  All  of  these  cases  will  not  be  considered,  for  it  is  easy  to 
draw  any  one  of  them  after  the  general  principle  has  been  made 
plain.  We  shall  content  ourselves  with  answering  the  following 


202  FUNDAMENTAL   PRINCIPLES   OF  CHEMISTRY 

question :  Are  the  phase  diagrams  which  result  from  the  assump- 
tion of  the  formation  of  a  new  substance  AB  different  from 
the  ordinary  solution  diagrams,  or  are  they  similar  to  them;  and 
if  they  are  similar,  to  what  extent  is  this  the  case  ?  The  answer 
to  this  question  will  enable  us  to  conclude  from  an  examination 
of  a  phase  diagram  whether  or  not  a  new  substance  AB  has  been 
formed. 

This  question  has  already  been  answered  as  far  as  its  general 
outlines  are  concerned.  In  many  cases  similar  diagrams  result 
from  the  formation  of  a  compound  and  from  the  formation  of  a 
solution.  The  formation  of  a  new  substance  is  therefore  neither 
proven  nor  excluded.  In  other  cases  new  phase  diagrams  will 
be  found,  and  when  this  is  the  case  it  may  be  concluded  that  a  new 
substance  has  been  formed.  There  are  no  phase  diagrams  which 
belong  only  to  solutions  and  which  do  not  belong  to  compounds. 
The  examination  of  the  phase  diagram  can  therefore  never  exclude 
the  possibility  that  a  new  substance  has  been  formed. 

The  Case  ggg.  —  Let  us  first  of  all  assume  that  the  two  original 
substances  A  and  B  are  gaseous,  and  that  they  can  form  a  com- 
pound AB  which  may  be  either  gaseous,  liquid,  or  solid.  The 
three  possibilities  we  shall  express  by  the  symbols  ggg,  gig,  and 
gsg,  the  newly  formed  state  being  placed  between  those  already 
existent.  The  corresponding  phase  diagrams  will  be  obtained 
by  combining  the  two  pairs.  The  case  gsg  is  made  up  of  two  gs 
phase  diagrams,  the  second  drawn  in  the  reverse  direction.  In 
the  diagrams  which  we  have  previously  considered  the  "  higher" 
state  has  always  been  placed  at  the  left  hand,  so  that  the  order 
has  been  gls.  If  the  succession  of  states  is  reversed,  right  and 
left  must  also  be  reversed  in  the  phase  diagram.. 

In  the  case  ggg  we  find  a  combination  of  two  gg  diagrams. 
According  to  Fig.  24,  which  is  repeated  for  the  sake  of  clearness 
as  Fig.  40,  three  different  gg  diagrams  are  possible,  and  these  must 
all  be  combined  in  every  possible  combination.  This  results  in 
six  cases,  I  I,  I  II,  I  III,  II II,  II  III,  and  III  III.  These  six 


ELEMENTS  AND   COMPOUNDS  203 

diagrams  are  all  shown  in  Fig.  41,  and  here  the  vertical  stroke  in 
the  middle  of  the  diagram  shows  the  proportions  of  A  and  B  in 
the  new  compound  AB.  This  is  only  mentioned  for  the  sake  of 


a 


FIG.  40. 

clearness,  for  of  course  we  do  not  know  as  yet  whether  the  sub- 
stance AB  has  been  produced  or  not,  and  this  can  only  be  deter- 
mined by  investigation. 

Comparison  of  the  diagrams  in  Fig.  41  with  those  of  Fig.  40 
will  show  that  all  the  cases  of  Fig.  40  are  present  in  Fig.  41.    They 


EL «---» 


V T -1 


' -i-l .--. 

VL r . 


FIG.  41. 


result  from  the  combination  of  the  simple  solution  line  I  of  Fig.  40 
with  7,  II,  or  777.  It  is  only  the  order  of  the  various  cases  and  not 
the  length  of  a  region  which  expresses  anything  definite  in  our 


204  FUNDAMENTAL  PRINCIPLES   OF  CHEMISTRY 

diagrams,  and  7,  II,  and  III  of  Fig.  41  are  therefore  identical 
with  I,  II,  and  777  of  Fig.  40  or  Fig.  24.  The  diagrams  IV,  V,  and 
VI  of  Fig.  41  are  new.  We  may  conclude  as  follows :  If  new  phase 
diagrams  of  the  form  ggg  IV,  V,  and  VI  are  found  for  two  gaseous 
substances  A  and  B,  a  new  substance  AB  has  been  produced. 
If  diagrams  similar  to  ggg  I,  II,  and  777  appear,  they  may  repre- 
sent either  chemical  combination  or  mere  solution. 

The  Case  gig.  —  If  a  liquid  is  formed  from  two  gases  the  corre- 
sponding phase  diagrams  result  from  an  exhaustive  combination 
of  the  gl  diagram  with  itself,  the  second  diagram  being  plotted 
in  the  reverse  direction  corresponding  to  Ig.  According  to  Fig.  27 
there  are  only  two  gl  cases,  and  these  can  give  three  combinations, 
1 1,  I  II,  and  77  77.  Corresponding  diagrams  are  shown  in  Fig. 


H T 


JJL r 1 


FIG.  42. 

42.  The  first  two  graphs  are  exactly  the  same  as  gg  II  and  777, 
so  that  in  these  cases  no  proof  is  to  be  had  of  the  formation  of  a 
new  substance.  777  is,  however,  new,  and  the  observation  of 
such  a  case  is  sufficient  ground  for  the  conclusion  that  a  new 
substance  has  been  formed. 

The  Case  gsg.  —  By  combination  of  the  five  gs  diagrams  fifteen 
possible  diagrams  may  result,  representing  a  solid  compound  pro- 
duced from  two  gases.  They  all  differ  from  previous  diagrams 
in  having  a  region  of  solid  phase  in  the  middle.  This  can  never 
be  the  case  for  a  mere  solution,  for  among  solutions  solid  phases 
can  only  appear  at  the  two  ends  of  the  diagram.  Every  addition 
results  in  lowering  the  melting  point  of  the  pure  substance,  that 
is,  in  the  formation  of  a  liquid  phase.  These  diagrams  are  further 


ELEMENTS  AND  COMPOUNDS 


205 


FIG.  43. 


206  FUNDAMENTAL  PRINCIPLES  OF  CHEMISTRY 

characterized  by  the  fact  that  at  the  point  indicating  the  relation 
in  which  A  and  B  combine  to  form  AB,  a  change  of  phase  occurs 
immediately  beside  the  solid  phase  AB.  All  possible  orders  of 
change  are  found,  from  gas  to  gas,  from  gas  to  liquid,  and  from 
liquid  to  liquid.  This  change  of  phase  takes  place  in  such  a  way 
that  the  proportional  content  of  the  changing  phase  decreases 
towards  zero  as  the  point  representing  the  composition  of  the  com- 
pound is  approached.  At  this  point  only  the  solid  phase  is  present, 
and  as  we  pass  away  from  it  the  new  phase  appears  at  first  in  very 
small  amount. 

Similar  conditions  will  appear  later  in  all  cases  where  the  prod- 
uct of  the  combination  of  A  and  B  is  a  solid.  In  these  cases  we 
can  therefore  recognise  with  certainty  the  formation  of  a  .compound. 
Not  only  that,  the  possibility  of  determining  the  composition  by 
weight  of  this  compound  (that  is,  the  ratio  of  A  to  B  in  it)  is  also 
given. 

The  Case  Igl.  —  Here  we  have  to  consider  the  same  diagrams  as 
in  the  case  gig,  that  is,  two  gl  diagrams.  In  this  case  they  must 
however  be  combined  in  the  reverse  sense.  The  gas  side  of  each 
must  be  turned  toward  the  other,  and  the  liquid  side  toward  the 
ends  of  the  diagrams. 

I 


n , , , i 


- — ^_. 

FIG.  44. 


Of  the  three  cases  shown  in  Fig.  44  the  first  two  will  be  found 
in  agreement  with  /////  and  IV.  They  can  therefore  not  serve 
to  indicate  a  chemical  process.  Ill  is  a  new  case,  and  it  can  there- 
fore serve  as  basis  for  the  conclusion  that  a  new  substance  has 
been  formed. 


ELEMENTS  AND   COMPOUNDS  207 

The  Case  III.  —  Ten  combinations  can  be  made  of  four  //  dia- 
grams, and  they  are  given  in  Fig.  45.  Five  of  them  7,  II,  HI,  IV, 
and  VI  correspond  to  four  of  the  //  diagrams,  and  IV  and  VI 
are  alike.  Five  others  are  new,  and  lead  to  the  conclusion  that 
new  compounds  are  formed. 


VI. 


I 1-..-. 


FIG.  45. 

It  will  be  noticed  that  II IV,  which  is  unsymmetrical,  and  which 
ends  in  a  liquid  phase  at  each  end,  can  be  combined  with  the  other 
diagrams  in  two  different  ways,  by  taking  it  either  forward  or  back- 
ward. If  this  peculiarity  is  taken  into  consideration  three  more 
diagrams  will  result.  These  diagrams  have  not  been  added,  for 


208  FUNDAMENTAL   PRINCIPLES   OF   CHEMISTRY 

they  would  merely  add  themselves  to  other  diagrams  characteristic 
of  the  formation  of  compounds,  and  would  therefore  give  no 
reason  for  question. 

The  Case  IsL  —  The  six  Is  cases  permit  of  twenty-one  combina- 
tions among  themselves,  and  this  is  the  number  of  diagrams  neces- 
sary to  represent  the  cases  which  may  arise  when  two  liquids 
combine  to  form  a  solid.  It  is  unnecessary  to  discuss  all  these 
diagrams,  for  in  each  of  these  cases  a  solid  phase  appears  in  the 
middle  and  none  at  the  ends  of  the  diagrams.  Such  diagrams  are 
excluded  for  solutions,  and  any  case  of  this  kind  leads  to  the  con- 
clusion that  a  new  substance  has  been  formed. 

The  Case  sqs.  —  This  case  also  is  made  up  of  combinations  of 

•7  A 

five  gs  diagrams  with  each  other,  giving  fifteen  individual  cases  in 
all.  It  differs  from  the  case  gsg  in  an  important  particular,  for 
here  we  no  longer  turn  the  ends  with  the  solid  phases  toward  each 
other,  but  those  with  gaseous  phases.  The  result  is  that  we  find 
repetition  of  several  diagrams  which  already  appeared  for  solutions 
under  the  case  ss.  It  is  therefore  necessary  to  present  a  com- 
plete series  of  diagrams  for  this  case,  and  these  are  shown  in 
Fig.  46. 

If  this  figure  is  compared  with  Fig.  26  it  will  be  found  that  all 
those  solution  diagrams  in  which  gases  appear  between  the  solid 
phases  are  represented  here.  These  are  II,  IX,  X,  III,  IV,  VII, 
and  VIII,  and  these  correspond  to  I -VI I  of  Fig.  26.  Diagrams 
VIII  to  XV  are  new,  and  can  be  used  as  an  indication  of  the 
presence  of  a  new  compound. 

This  large  number  of  cases  does  not  correspond  to  any  particular 
experimental  fact  of  value.  The  great  majority  of  chemical  pro- 
cesses take  place  in  such  way  that  liquids  or  solids  are  formed 
from  gases,  or  solids  are  formed  from  liquids,  and  reactions  in  the 
inverse  sense  are  rare.  The  formation  of  a  gas  from  solid  ma- 
terials is  the  rarest  of  all.  Processes  of  this  sort  are  most  usual  at 
high  temperatures. 

The  Case  sis.  —  We  found  six  Is  diagrams  and  a  complete  set 


ELEMENTS  AND   COMPOUNDS 


210  FUNDAMENTAL  PRINCIPLES  OF  CHEMISTRY 

of  combinations  of  these  results  in  a  total  of  twenty-one  cases.    For 
the  case  Isl  we  found  it  unnecessary  to  discuss  the  individual  cases, 


m 


JV 


VI 


VOL 


IX 


FIG.  47. 


and  it  was  merely  necessary  to  say  that  agreement  with  the  solution 
diagrams  was  impossible.     In  this  case,  where  the  solid  phases 


ELEMENTS   AND   COMPOUNDS  211 

appear  at  the  edges  of  the  diagram  and  not  in  the  middle,  agree- 
ment with  some  of  the  solution  cases  is  certain  to  be  found. 

Even  in  this  case,  however,  it  is  not  necessary  to  examine  all 
the  cases  indicated.  We  have  only  to  look  for  agreement  with  the 
ss  diagrams,  and  the  following  reasoning  is  sufficient.  In  Fig.  26 
the  greatest  number  of  two  phase  regions  which  can  occur  in  a 
diagram  is  five  (in  IV).  Out  of  all  the  possible  diagrams  for  sis 
we  therefore  need  to  examine  only  those  in  which  not  more  than 
five  double  lines  indicating  two  phase  regions  occur.  This  limits 
our  investigation  to  thirteen  diagrams,  and  these  are  shown  in 
Fig.  47. 

Only  two  of  these  diagrams  are  new,  VII  and  XI;  the  others 
will  all  be  found  under  ss.  It  will  also  be  noticed  that  two  dia- 
grams occur  twice  in  the  same  form,  IV  and  VIII,  and  VI  and  IX. 
They  differ  only  in  the  position  of  the  point  corresponding  to  the 
formation  of  a  new  compound.  It  will  be  seen  from  this  that  dia- 
grams like  these  are  not  of  assistance  in  deciding  whether  a  com- 
pound has  been  formed  or  not.  Not  only  this ;  even  when  the  fact 
of  formation  of  a  compound  has  been  found  in  other  ways,  such 
diagrams  do  not  even  permit  of  the  determination  of  the  region  in 
which  the  new  substance  would  appear.  In  all  the  earlier  cases 
the  diagrams  could  at  least  assist  in  this  latter  way. 

The  Case  sss.  —  A  complete  set  of  combinations  of  the  ten  ss 
cases  with  each  other  would  result  in  fifty-five  diagrams.  In  every 
case,  however,  a  solid  phase  appears  in  the  middle  of  each  diagram, 
and  this  means  that  no  solution  diagram  whatever  can  be  similar  to 
any  one  of  them.  Even  when  no  liquid  or  gaseous  phase  appears 
in  the  diagram,  so  that  through  the  whole  set  of  proportions  of  A 
to  B  only  solid  phases  are  present,  the  diagram  corresponding  to 
the  appearance  of  a  solid  compound  AB  is  different  from  the  one 
which  represents  a  mere  solid  mixture  of  A  and  B.  Fig.  48  shows 
the  corresponding  phase  diagrams.  II  is  the  case  where  a  solid 
compound  appears ;  I  represents  a  mere  mixture.  The  shift  in  the 
heavy  line  in  II  expresses  the  fact  that  at  this  point  one  solid  phase 


212  FUNDAMENTAL   PRINCIPLES   OF   CHEMISTRY 

disappears  and  another  takes  its  place.  If  A  and  B  were  mixed 
together  in  the  proportions  represented  by  this  point  a  single  solid 
phase  would  result,  the  compound  AB.  For  any  other  proportions 


FIG.  48. 

mixtures  of  AB  with  A  or  B  will  occur.  All  this  is  evidently  wholly 
different  from  the  case  where  no  compound  appears.  In  this  case 
no  finite  proportion  of  the  two  substances  could  be  found  cor- 
responding to  the  presence  of  only  one  solid  phase. 

The  Case  ggl.  —  This  combination  is  the  first  of  the  second 
group  of  phase  diagrams  in  which  a  new  substance  is  formed  from 
two  constituents  in  different  states.  In  this  case  therefore  it  is 
no  longer  the  individual  cases  of  a  single  group  which  are  to  be 
combined  with  each  other,  but  cases  from  two  groups.  The  number 
of  combinations  will  therefore  no  longer  be  found  with  the  aid  of 
the  series  1  +2  +  3  +  .  .  .  +n,  where  n  is  the  number  of  cases  in  the 
group.  The  number  of  combinations  will  be  given  by  the  product 
mn,  where  m  and  n  are  the  number  of  cases  in  the  two  groups  in 
question. 

In  the  case  ggl  groups  gg  and  gl  take  part.  The  number  of 
cases  is  therefore  3x2  =  6,  and  they  are  shown  in  Fig.  49.  Com- 
parison with  the  solution  diagrams  gl  will  show  that  these  appear 
again  (7  and  77),  but  the  four  other  diagrams  are  new. 

The  Case  gll.  —  It  is  unnecessary  to  present  the  ten  diagrams 
corresponding  to  this  case  in  order  to  understand  clearly  the  result 
of  these  combinations.  The  addition  of  the  continuous  liquid  line 
of  Fig.  25  7  to  the  two  gl  diagrams  leaves  the  latter  unchanged, 
and  these  diagrams  will  be  found  to  describe  cases  in  which  com- 
bination occurs.  The  eight  other  cases  are  all  more  complicated 
and  afford  proof  of  the  appearance  of  a  compound. 


ELEMENTS  AND  COMPOUNDS  213 

The  Case  gsl.  —  In  every  case  when  a  compound  is  a  solid  new 
diagrams  appear.  This  case  would  include  in  all  5  X  6  =  30  new 
diagrams,  which  it  is  unnecessary  to  present. 

The  Case  ggs.  —  The  addition  of  the  continuous  gas  line  gg  I 
to  the  five  gs  diagrams  gives  five  cases  which  agree  formally  with 


m 


-ra— I- -i 

VZ Tzzza — , ,  i 


-T > 

FIG.  49. 

the  solution  diagrams  gs,  and  are  therefore  of  no  value  as  criteria. 
In  the  same  way  the  addition  of  gs  I  to  the  three  gg  cases  gives 
diagrams  which  are  all  repetitions.  Seven  of  the  fifteen  diagrams 
in  this  case  are  similar  to  corresponding  solution  diagrams.  The 
eight  others  are  new  and  characteristic  of  chemical  combination. 

The  Case  gls.  —  Four  of  the  twelve  possible  cases  are  like  solu- 
tion diagrams  gs,  II  to  V.  The  solution  diagram  gs  I  is  not  re- 
peated in  this  case,  since  it  contains  no  liquid  phase. 

The  Case  gss.  —  The  fifteen  different  possible  cases  contain 
no  case  which  is  like  a  solution  diagram,  and  this  is  because  the 
solid  phase  occurs  in  the  middle  of  the  diagram. 

The  Case  Igs.  —  Four  of  the  ten  cases  are  like  solutions  Is,  and 
these  are  all  the  cases  in  which  a  gas  phase  can  appear  between 


214  FUNDAMENTAL   PRINCIPLES   OF   CHEMISTRY 

a  solid  and  a  liquid  in  a  solution  diagram.  The  six  other  cases  are 
new  and  characteristic  of  chemical  combination. 

The  Case  Us.  —  Eleven  of  the  twenty-four  diagrams  which 
result  by  combining  //  with  Is  correspond  to  solution  dia- 
grams, and  many  repetitions  are  found.  The  other  diagrams 
are  new. 

The  Case  Iss.  —  The  sixty  diagrams  of  this  group  are  new,  as  is 
always  the  case  when  the  compound  is  a  solid. 

144.  SUMMARY.  —  A  general  review  of  the  possible  cases  of  a 
binary  chemical  combination  shows  that  all  the  phase  diagrams 
corresponding  to  a  mere  mutual  solution  of  the  substances  involved 
can  also  appear  when  chemical  combination  has  taken  place  be- 
tween the  two  substances.  The  only  exception  to  this  case  will  be 
found  in  the  fact  that  two  solids  can  form  a  mixture  without  ex- 
erting any  influence  on  each  other.  The  phase  diagram  of  a  solution 
contains  no  answer  to  the  question  whether  mere  solution  or  chemi- 
cal combination  has  taken  place.  There  are,  however,  a  large 
number  of  more  complex  diagrams  which  do  afford  a  criterion  of 
the  appearance  of  a  chemical  compound.  The  clearest  cases  of  all 
are  those  in  which  solid  substances  are  formed.  In  this  case  the 
phase  diagram  is  always  different  from  a  solution  diagram,  and 
in  this  case  it  is  always  possible  to  determine  the  composition  of 
the  new  substance  in  terms  of  its  constituents.  It  is  evident  from 
this  that  the  question  whether  a  new  substance  has  been  formed 
or  not  can  best  be  answered  by  investigating  the  matter  under  such 
experimental  conditions  as  will  probably  yield  a  solid  phase.  It 
is  usually  best  to  have  recourse  to  high  temperatures  to  bring  about 
chemical  processes,  and  this  is  principally  because  reaction  veloci- 
ties are  increased  in  this  way.  For  the  isolation  and  purification 
of  substances  low  temperatures  will  lead  much  more  certainly  and 
rapidly  to  the  desired  end.  This  statement  must  be  made  with  a 
reservation  that  we  do  not  pass  out  of  the  region  of  stability  of  the 
new  substance  when  the  temperature  is  lowered.  The  region  of 
stability  of  most  substances  is  practically  unlimited  in  the  direction 


ELEMENTS  AND   COMPOUNDS  215 

of  lower  temperature,  so  that  the  reservation  just  made  is  really 
not  so  important. 

The  certainty  to  be  derived  from  those  cases  where  solid  phases 
appear  depends  upon  the  fact  that  no  solutions  are  formed  among 
solids.  At  any  rate  we  have  assumed  this  to  be  the  case.  It  is, 
of  course,  possible  that  in  the  other  states  the  solubility  may  be 
so  small  as  to  be  unmeasurable,  and  in  this  case  a  result  precisely 
similar  to  that  found  for  solids  is  to  be  expected.  The  correspond- 
ing phase  diagrams  will  be  changed,  and  the  regions  corresponding 
to  solutions  of  a  single  phase,  which  we  have  in  general  assumed 
to  be  of  finite  range,  will  all  disappear.  In  their  place  regions  of 
two  phases  will  extend  to  the  point  corresponding  to  the  proportions 
of  the  compound  formed,  and  at  this  point  a  sudden  shift  will  take 
place,  one  of  the  phases  disappearing  and  another  taking  its  place. 

To  make  this  clear  let  us  take  a  concrete  example,  the  diagram 
ggl  II  on  page  213.  Here  we  have  assumed  that  both  the  gas  A 
and  the  liquid  B  have  a  measurable  solubility  in  the  new-formed 
liquid.  If  we  assume  instead  that  both  are  practically  insoluble  in 
AB,  the  diagram  changes  into  II  of  Fig.  50,  the  two  two-phase 


m 


FIG.  50. 


regions  approaching  each  other  until  they  meet  at  the  point  cor- 
responding to  the  compound.  It  is  evident  that  in  such  a  case  the 
proportions  of  combination  may  be  deduced  directly  from  a  study 
of  the  phases  involved.  If  practical  insolubility  occurs  for  one 
constituent,  the  corresponding  region  of  two  phases  moves  up  to 
the  point  representing  the  proportions  of  combination.  In  such  a 
case  (Fig.  50  ///)  a  knowledge  of  the  solubility  relations  is  neces- 


216  FUNDAMENTAL  PRINCIPLES  OF  CHEMISTRY 

sary  if  any  evidence  on  this  point  is  to  be  obtained  from  the  phase 
diagram.  Such  knowledge  of  solubility  cannot,  in  general,  be 
assumed,  and  without  it  the  phase  diagram  remains  just  as  indeter- 
minate as  in  the  general  case. 

145.  THE  EFFECT  OF  TEMPERATURE.  —  In  Sec.  126  we  dis- 
cussed the  effect  of  temperature  on  the  phase  diagrams  represent- 
ing simple  solution,  and  we  have  now  to  answer  the  more  general 
question  as  to  its  effect  in  the  more  complex  case  of  phase  diagrams 
in  which  chemical  combination  takes  place. 

It  may  be  said  in  general  that  these  diagrams  can  be  considered 
combinations  of  the  two  individual  diagrams,  as  in  the  case  of  the 
isothermals.  It  would  be  difficult  to  exhaust  all  the  possibilities 
in  this  way.  It  is  also  unnecessary,  for  the  whole  interest  of  the 
question  is  confined  to  the  peculiarities  of  the  middle  part  of  the 
diagram,  where  the  compound  appears. 

In  this  middle  part  there  will  be  found  a  point  corresponding  to 
the  appearance  of  the  compound  as  a  pure  substance.  This  point 
will  lie  where  A  and  B  are  chosen  in  such  proportions  that  the 
compound  AB  is  formed  from  them  without  any  remainder  or 
excess.  On  both  sides  of  this  point  either  A  or  B  appears  in  excess. 
When  a  gas  or  a  liquid  occupies  the  centre  of  the  diagram  a  con- 
tinuous series  of  solutions  results.  When  AB  is  a  solid  we  find  a 
pure  solid  substance  at  this  point,  and  on  either  side  of  it  may  be 
found  new  phases  of  any  state. 

From  this  point  of  view  the  three  kinds  of  curves  which  need  to 
be  considered  offer  no  difficulties.  Two  boiling  point  curves  may 
meet  at  the  point  AB.  Two  melting  point  curves  or  two  sublima- 
tion curves,  or  finally  one  melting  point  and  one  sublimation  curve, 
may  also  meet  at  this  point.  The  last  two  types  cannot  meet  a 
boiling  point  curve,  for  the  solid  phase  lies  at  both  sides  of  the 
point  AB,  if  it  touches  this  point  at  all. 

When  two  boiling  point  curves  meet,  diagrams  like  those  in  Fig. 
51  result.  They  are  characterized  by  the  fact  that  the  liquid  at  the 
point  AB  behaves  like  a  pure  substance.  This  is  because  two 


ELEMENTS   AND   COMPOUNDS 


217 


limits  of  the  two-phase  regions  lie  at  this  point,  and  the  vapour 
has  the  same  composition  as  the  liquid.  The  two  regions  and  the 
lines  which  bound  them  meet 
at  the  point  AB  at  a  finite 
angle.  There  is  always  a 
kink  at  this  point,  and  the 
curves  can  never  be  contin- 
uous. If  a  series  of  liquids, 
chosen  from  this  middle 
region  (or  in  general  from 
any  region  of  one  phase 
which  does  not  lie  at  the 


FIG.  51. 


end    of    the    diagram),  are 

examined   by  boiling  them, 

it  is  possible  to  find  out  whether  a  point  AB  corresponding  to  a 

compound  exists  in  this  region  or  not,  and,  if  such  a  point  exists, 

what  its  composition  is. 

The  proof  is  of  course  easiest  when  the  point  AB  represents  at 
the  same  time  a  singular  value,  as  in  Fig.  51  //  and  777.  Even  in 
case  /  conditions  may  be  such  that  no  doubt  will  remain  as  to  the 
presence  of  an  angle  between  the  curves.  Under  all  circumstances 
the  behaviour  of  these  liquids  during  distillation  and  the  proof  of  a 
constant  boiling  point  in  the  one-sided  boiling  curves  is  sufficient 
evidence  of  the  presence  of  a  compound. 

Comparison  of  Fig.  51  with  the  boiling  point  curves  in  Figs.  9 
and  11  for  simple  solutions  shows  their  external  similarity.  The 
study  of  isothermal  phase  diagrams  in  such  cases  is  not  always 
sufficient  to  determine  a  decision.  The  cases  II  and  777  are 
specially  similar,  for  the  liquids  corresponding  to  singular  points 
on  the  boiling  point  curves  are  hylotropic,  and  can  therefore  be 
distilled  at  constant  temperature.  The  distinction  between  solu- 
tion and  compound  is  therefore  to  be  sought  in  the  fact  that  the 
boiling  point  curve  for  the  solution  is  continuous,  while  that  for 
the  compound  has  a  kink  in  it.  Another  difference  depends  on 


218 


FUNDAMENTAL  PRINCIPLES  OF  CHEMISTRY 


the  fact  that  a  singular  point  belonging  to  a  compound  is  always 
independent  of  the  temperature,  even  though  this  be  varied  within 
wide  limits  by  changing  the  pressure.  Singular  points  of  solutions 
change  their  position  (composition)  with  a  change  in  temperature, 
as  will  be  explained  more  fully  later.  It  will  be  found  when  we 
come  to  this  point  that  the  composition  A :  B  of  a  compound  is  not 
affected  by  temperature  as  long  as  we  do  not  leave  the  region  of 
stability  of  the  substance  in  question. 

In  the  cases  just  discussed  we  found  that  the  isothermal  phase 
diagrams  often  left  us  without  any  answer  to  the  question :  is 
this  a  solution  or  is  it  a  compound  ?  If,  however,  the  investiga- 
tion is  carried  through  a  whole  series  of  temperatures  (and  of 
pressures  also  when  this  is  necessary)  a  definite  answer  can  always 
be  found.  Even  this  is  only  generally  true  when  A  and  B  unite 
completely  to  form  the  compound  AB.  If  this  condition  is  not 
fulfilled,  if  the  combination  is  not  complete  and  a  case  of  homo- 
geneous equilibrium  between  the  compound  and  its  constituents 
results,  this  test  also  must  fail.  In  place  of  the  pure  substance  a 
solution  of  A,  B,  and  AB  is  formed  at  the  point  AB.  When  this  is 

distilled  it  acts  like  a  solu- 
tion, and  the  kink  at  AB  is  re- 
placed by  a  rounded  curve. 
The  matter  is  simpler 
when  AB  is  a  solid.  The 
melting  point  curve  is  then 
made  up  by  connecting 
two  melting  point  curves 
of  the  typical  form  shown 
in  Fig.  17.  A  curve  like 

that  of  Fig.  52  results,  a  zigzag,  with  a  highest  point  corresponding 
to  the  melting  point  of  the  pure  substance,  and  a  lowest  singular 
point  corresponding  to  the  eutectic  of  the  neighbouring  sub- 
stances. Attention  should  be  called  to  the  fact  that  even  when 
several  compounds  appear  between  A  and  B,  the  only  effect  is  to 


FIG.  52. 


ELEMENTS  AND   COMPOUNDS 


219 


make  the  zigzag  line  more  complicated.  The  number  of  upper 
points  which  appears  indicates  the  number  of  compounds  between 
A  and  B. 

A  conclusion  previously  found  for  the  case  of  chemical  equilibrium 
may  be  repeated  here,  but  it  can  only  be  applied  to  the  liquid  phase 
(homogeneous  equilibrium  between  solids  is  excluded  by  defini- 
tion). The  point  is  this:  the  compound  AB  can  exist  in  solid 
form,  but  when  it  melts  we  have  a  solution  of  A,  AB,  and  B.  The 
result  is  that  in  place  of  the 
sharp  angle  of  Fig.  52  we  find 
a  rounded  curve  and  a  rela- 
tion to  the  ideal  line  which 
is  shown  in  Fig.  53. 

The  sublimation  curves  can 
be  treated  in  a  precisely 
similar  way,  and  they  will 
be  found  to  agree  in  all 
points  with  the  typical  melt- 
ing point  curves. 

This  covers  the  further  case  in  which  a  melting  point  curve  ends 
on  one  side  at  AB  and  a  sublimation  curve  at  the  other. 

In  any  of  these  cases  the  isothermal  phase  diagram  must  decide 
the  question  of  the  existence  and  composition  of  a  compound. 
The  temperature  diagram  can  only  confirm  the  matter.  Never- 
theless it  will  be  found  that  the  investigation  of  temperature  curves 
is  one  of  the  most  efficient  means  of  deciding  such  a  question. 

146.  MORE  GENERAL  CONDITIONS.  —  We  shall  now  lay  aside 
our  assumption  that  phase  diagrams  are  to  be  used  exclusively 
in  deciding  whether  or  not  a  new  compound  will  appear.  And 
we  shall  also  lay  aside  the  assumption  that  temperature  and  pres- 
sure shall  remain  unaltered.  Our  previous  discussion  has  given 
us  one  advantage :  we  have  settled  all  the  cases  in  which  the  phase 
diagram  alone  can  lead  us  to  a  definite  conclusion,  and  we  need 
therefore  only  discuss  those  cases  in  which  the  phase  diagram  of 


FIG.  53. 


220  FUNDAMENTAL   PRINCIPLES  OF  CHEMISTRY 

a  true  chemical  process  is  similar  to  that  of  a  mere  solution.  We 
must  now  find  out  what  other  means  can  be  applied  to  the  solu- 
tion of  the  same  problem,  and  also  how  we  can  decide  about  tht 
proportion  in  which  A  and  B  will  combine  to  form  the  new  com- 
pound substance  AB. 

A  similar  discussion  will  be  applicable  in  those  cases  where  the 
phase  diagram  indicates  the  existence  of  a  new  compound,  but 
says  nothing  about  its  composition. 

147.  Two  GASES.  — •  The  general  and  most  usual  condition  in 
the  case  of  two  gases  is  the  formation  of  a  solution,  no  matter  what 
the  proportions  of  the  gases  may  be.  This  cannot  be  distinguished 
from  the  case  of  Sec.  132,  the  formation  of  a  gaseous  compound, 
if  we  assume  that  all  the  substances  which  take  part  are  so  far 
removed  from  their  critical  point  that  the  appearance  of  a  liquid 
phase  is  excluded.  We  might  try  to  decide  whether  or  not  a  gaseous 
compound  AB  has  been  produced  by  lowering  the  temperature 
until  the  region  of  liquid  and  solid  phases  is  reached.  This  would 
not  exclude  the  possibility  that  the  compound  might  first  be  formed 
at  this  lower  temperature.  In  other  words,  the  region  of  stability 
of  the  compound  may  lie  below  the  temperature  of  our  experi- 
ment. We  must  see  whether  it  is  not  possible  to  decide  the  ques- 
tion of  the  formation  of  a  new  substance  directly  in  the  gaseous 
system,  without  a  change  of  temperature  or  pressure,  by  the  aid 
of  some  other  characteristic.  As  a  matter  of  fact  it  is  possible  to 
decide  this  question  in  every  case. 

The  question  can  be  decided  in  the  case  of  gases  with  the  aid 
of  the  law  of  Sec.  83.  According  to  this  law  all  the  properties  of 
a  gaseous  solution  can  be  determined  by  properly  taking  the  sum 
of  the  properties  of  its  constituents.  Whenever  measurement 
shows  that  this  law  does  not  hold  true,  the  formation  of  a  new 
constituent  must  be  concluded. 

Let  us  investigate  the  value  of  any  property  first  in  the  pure 
constituent  A,  then  in  solutions  made  up  of  0.9  A  and  0.1  B,  of 
0.8  A  and  0.2  5,  etc.,  and  finally  of  pure  B.  We  will  now  lay  off 


ELEMENTS  AND  COMPOUNDS  221 

the  measured  values  along  lines  drawn  perpendicular  to  a  hori- 
zontal line  divided  into  ten  equal  parts.  The  law  of  gas  solutions 
may  now  be  expressed  by  saying  that  the  individual  points  repre- 
senting the  values  of  the  property  in  the  different  solutions  all  lie 
on  a  straight  line  joining  the  points  representing  the  value  of  the 
property  in  the  free  constituents.  It  must  be  kept  in  mind  that 
such  specific  properties  as  are  based  upon  the  unit  of  weight  must  be 
determined  in  solutions  whose  composition  is  determined  by  weight, 
and  in  case  the  property  is  based  upon  the  unit  of  volume  the  com- 
position of  the  various  solutions  must  be  determined  by  volume. 

Volume  itself  affords  a  simple  example  when  pressure  and  tem- 
perature are  kept  constant.  If  we  investigate  the  volume  of  dif- 
ferent solutions  of  A  and  B,  made  up  as  described  above,  the  volume 
of  the  solutions  will  be  found  equal  to  the  sum  of  the  partial  volumes 


a 


FIG.  54. 

of  the  constituents.  If  a  is  the  volume  of  A,  and  if  tenths  of  A  are 
replaced  one  after  the  other  by  an  equal  volume  of  B,  the  total 
volume  remains  unchanged  in  case  no  new  substance  appears. 
All  the  volume  points  lie  at  an  equal  height,  and  the  result  is  a 
diagram  like  that  of  Fig.  54. 


222  FUNDAMENTAL   PRINCIPLES   OF  CHEMISTRY 

If  a  change  in  the  total  volume  takes  place,  so  that  the  hori- 
zontal line  is  replaced  by  any  other  line,  a  new  substance  has  been 
produced. 

The  converse  of  this  does  not  always  hold.  There  are  cases 
where  the  total  volume  remains  unchanged  even  though  a  new 
substance  is  formed.  In  these  cases,  however,  deviations  from 
the  solution  law  for  gases  appear,  and  in  general  we  will  find 
change  in  all  the  specific  properties  which  are  capable  of  change.* 

If  none  of  the  properties  shows  any  deviation  from  the  simple 
summation  law,  no  new  substance  can  have  been  produced. 

In  cases  not  so  simple  as  the  one  just  discussed  we  shall  have 
in  general  the  following  conditions:  a  represents  the  value  of  the 
property  in  pure  A,  and  b  the  value  in  pure  B.  In  all  solutions  of 
A  and  B  this  property  will  exhibit  the  values  represented  by  the 
points  on  the  line  ab  in  Fig.  55.  It  will  of  course  occur  that  the 
property  will  have  zero  value  in  one  of  the  gases,  as,  for  example, 
when  one  of  the  gases  is  coloured  and  the  other  colourless.  In 
this  case  a  or  b  will  lie  on  the  line  of  abscissas,  as  represented  by 
the  lower  line  in  Fig.  55. 

The  shape  which  the  line  ab  assumes  in  case  a  pure  new  com- 
pound is  formed  may  be  found  from  a  consideration  of  the  fact 
that  the  new  gaseous  substance  will  form  solutions  with  the  original 
gases.  The  gaseous  system  will  then  be  made  up  of  the  new  gas 
with  an  excess  of  A  or  B,  and  it  will  therefore  have  a  correspond- 
ing set  of  properties.  Let  us  begin  with  pure  A  and  add  to  this 
a  small  amount  of  B.  This  will  react  with  A,  changing  com- 
pletely into  the  new  substance,  which  we  will  call  AB.  AB  will 
form  a  solution  with  the  unchanged  part  of  A,  and  our  familiar 
laws  can  all  be  applied  to  this  system.  If  more  B  be  added  the 
same  process  takes  place,  but  the  fraction  AB  becomes  larger 

*  We  find  here  an  exception  from  the  general  law  that  when  a  change  takes 
place  in  a  substance  all  properties  show  a  change  in  value  at  the  same  time* 
We  know  already  that  mass  and  weight  remain  unchanged  under  all  circum- 
stances, even  when  the  most  far-reaching  chemical  changes  have  taken  place. 
In  the  special  case  before  us  we  see  that  volume  also  shows  this  peculiarity. 


ELEMENTS  AND   COMPOUNDS 


223 


compared  to  A.  Continuing  in  the  same  way  we  must  finally 
arrive  at  a  point  where  all  of  A  has  combined  with  B  and  where 
no  excess  of  B  is  present.  The  gaseous  system  then  consists  of 
a  pure  new  substance  AB.  Further  additions  of  B  result  in  solu- 
tions of  AB  and  B,  and  the  end  of  the  series  is  pure  B. 

It  will  be  evident  that  the  entire  diagram  which  represents  what 
has  taken  place  is  made  up  of  two  parts,  each  of  which  can  be 


FIG.  55. 

represented  by  a  straight  line  like  that  of  Fig.  55.  These  two 
straight  lines  cut  each  other  at  a  definite  angle  acb,  Fig.  56.  If  acb 
were  a  straight  line,  this  property  of  the  gas  AB  would  indicate  a 
mere  solution  of  the  two  gases,  and  this  we  have  excluded  in  this 
case.  Whether  the  two  straight  lines  are  inclined  to  each  other 
in  this  sense  or  in  the  opposite,  as  shown  in  Fig.  57,  depends  upon 
the  special  values  of  the  property  under  investigation.  Experi- 
mental investigation  usually  shows  figures  like  those  just  described. 
Occasionally  curved  lines  take  the  place  of  the  straight  ones,  giv- 
ing a  diagram  like  that  of  Fig.  56,  with  the  sharp  corner  where 


224  FUNDAMENTAL  PRINCIPLES  OF  CHEMISTRY 

the  two  lines  meet  rounded  off  into  a  smooth  curve.  Cases  of  this 
sort  show  a  varying  behaviour  which  is  of  importance  when  constit- 
uents are  to  be  separated,  and  when  they  appear  we  must  conclude 
that  the  combination  of  A  and  B  to  AB  is  incomplete.  Uncom- 
bined  fractions  of  A  and  B  can  exist  together  with  the  compound 
AB,  all  forming  a  solution  together.  We  shall  not  take  up  the 
discussion  of  these  more  difficult  cases  at  this  point.  For  the 


1 1 H-H 1 I 


FIG.  56. 

present  we  will  confine  ourselves  expressly  to  cases  where  th 
combination  of  A  and  B  in  the  proper  proportions  is  practically 
complete. 

148.  ENERGY  CONTENT.  —  Every  substance  has  an  energy 
content,  and  this  is  a  definite  value  for  every  gas.  We  have  no  way 
of  determining  its  total  value,  for  no  substance  exists  which  is 
quite  free  from  energy,  but  we  can  measure  differences  in  energy 
content  corresponding  to  given  differences  in  the  condition  of  a 
system.  It  is  almost  always  possible  to  conduct  an  experiment  in 
such  a  way  that  this  energy  difference  appears  as  heat,  so  that 
measurement  of  the  quantity  of  heat  which  enters  or  leaves  the 
system  gives  us  the  desired  difference  directly.  The  total  energy 
of  a  gas  solution  is  the  sum  of  the  partial  energies  of  its  constit- 


ELEMENTS  AND   COMPOUNDS  225 

uents.  We  may  conclude  from  this  that  a  mere  change  in  volume 
of  a  gas,  without  the  performance  of  external  work,  results  in  no 
change  in  its  total  energy.  This  means  that  when  gases  which 
form  solutions  and  not  compounds  with  one  another  are  mixed 
together,  no  heat  exchange  results,  provided  pressure  and  tem- 
perature were  the  same  when  the  gases  were  mixed.  Conversely, 


H r 


FIG.  57. 


the  appearance  of  a  measurable  heat  exchange  when  two  gases 
are  mixed  is  a  sure  sign  that  a  chemical  process  in  the  narrower 
sense  has  taken  place ;  that  is,  a  new  substance  has  been  formed. 

The  diagrammatic  representation  of  this  process  is  therefore 
similar  to  that  of  the  previously  described  general  one.  In  Fig. 
56,  a  represents  the  energy  of  the  gas  A,  and  b  that  of  B.  Then  any 
solution  of  A  and  B  will  possess  an  energy  content  which  can  be 
represented  by  a  corresponding  point  on  the  straight  line  ab.  If 
a  compound  AB  is  formed  we  will  have  two  straight  lines  ac  and 
cb  meeting  each  other  at  an  angle.  In  the  majority  of  cases  this 
angle  lies  below  the  straight  line  ab  in  Fig.  56,  and  this  expresses 
the  fact  that  the  majority  of  reactions  between  gases  result  in  the 

15 


226  FUNDAMENTAL   PRINCIPLES   OF  CHEMISTRY 

giving  out  of  energy.  The  immediate  result  of  this  is  an  increase 
in  the  temperature  of  the  system,  and  in  order  to  restore  the  orig- 
inal temperature  a  corresponding  amount  of  heat  must  be  with- 
drawn. If  we  merely  wish  to  prove  the  fact  of  the  heat  exchange, 
and  not  to  measure  it  exactly,  it  is  only  necessary  to  observe  the 
temperature  of  the  gas  after  mixing  A  and  B.  If  the  temperature 
is  the  same  as  before  mixture  we  have  a  solution.  If  it  has  changed, 
a  compound  has  been  formed. 

149.  THE  LAW  OF  CONSTANT  PROPORTIONS.  —  It  is  evident 
from  the  diagram  representing  the  process  by  which  the  compound 
AB  is  formed  from  the  substances  A  and  B,  that  the  combination 
of  A  and  B  takes  place  in  a  definite  proportion  by  volume,  and 
therefore  in  a  definite  proportion  by  weight.  This  holds  at  least 
for 'this  individual  experiment.  We  may  conclude  that  the  rela- 
tion thus  indicated  by  one  experiment  will  hold  for  all  subsequent 
experiments  under  the  same  conditions.  Our  assumption  was 
that  A  and  B  are  pure  substances,  meaning  by  this  that  they  were 
substances  with  perfectly  definite  specific  pfoperties.  The  same 
assumption  is  true  of  the  compound  AB.  Properties  are  functions 
of  composition,  and  therefore  constancy  in  the  properties  of  AB 
corresponds  to  constancy  in  the  proportion  in  which  A  and  B 
combine  to  form  AB. 

The  question  then  arises  whether  this  proportion  will  remain 
the  same  at  other  temperatures  and  pressures.  This  question  we 
can  answer  in  the  affirmative  if  we  confine  ourselves  to  a  certain 
range  of  conditions,  as  will  be  evident  from  what  follows. 

A  pure  substance  retains  its  properties  within  a  finite  range  of 
pressures  and  temperatmes.  In  other  words,  there  are  limits  of 
temperature  and  pressure  within  which  a  pure  substance  does  not 
assume  the  properties  of  a  solution.  The  substance  AB  will  there- 
fore behave  like  a  pure  substance  within  a  definite  region.  This 
means  that  any  endeavour  to  break  it  up  by  ordinary  methods 
of  phase  separation  will  show  it  to  be  hylotropic,  and  that  it  will 
pass  as  a  whole  into  other  states  or  phases.  This  is  merely  another 


ELEMENTS  AND   COMPOUNDS  227 

way  of  saying  that  within  this  region  the  substance  is  formed  from 
A  and  B  in  constant  proportions,  for  if  the  proportion  were  variable 
with  temperature,  so  that,  for  example,  at  higher  temperature  less 
A  and  more  B  would  combine,  we  could  form  AB  at  this  tempera- 
ture, and  then  cool  it  down  in  its  pure  condition  to  the  original 
temperature.  If  it  took  on  its  original  composition  at  the  lower 
temperature,  a  corresponding  amount  of  uncombined  B  must 
separate  and  we  would  have  a  solution.  This  contradicts  the  as- 
sumption that  AB  is  a  pure  substance,  —  one  which  retains  its 
character  regardless  of  change  in  temperature.  The  conclusion 
is  that  AB  must  have  a  constant  composition  at  all  temperatures 
and  pressures  within  its  region  of  stability. 

This  law  is  called  the  law  of  constant  proportions  or  the  law  of 
constant  relations.  We  have  proven  it  for  gases,  and  we  have 
shown  that  the  concept  of  a  pure  substance  contains  the  assump- 
tion that  its  composition  remains  unchanged  within  its  region  of 
stability.  The  reasoning  is  the  same  when  pure  substances  in  liquid 
or  solid  form  are  considered  instead  of  gases,  and  the  proof  is  a 
general  one.  In  other  words,  since  nothing  is  said  of  the  state  of 
the  substance  in  our  assumptions  and  conclusions,  the  proof  is 
independent  of  state  and  therefore  holds  for  all  the  states.  The 
general  expression  is  therefore:  whenever  a  compound  pure  sub- 
stance AB  is  produced  from  two  pure  substances  A  and  B,  the 
proportion  by  weight  of  A  and  B  which  is  necessary  to  form 
AB  is  constant  within  the  common  range  of  stability  of  the  three 
substances. 

The  cases  represented  in  77  and  ///,  Fig.  40,  remain  to  be  con- 
sidered. To  decide  in  these  cases  whether  we  have  to  do  with  a 
solution  or  a  gaseous  compound  we  need  only  apply  what  we  have 
just  learned  in  the  middle  gaseous  region  where  the  compound  will 
appear  if  one  is  formed.  If  this  test  gives  a  positive  or  a  negative 
result,  the  general  question  is  answered  in  the  same  sense.  Any 
similar  cases  which  may  appear  later  can  be  answered  in  the  same 
way.  It  will,  in  general,  be  sufficient  to  investigate  the  simplest 


228  FUNDAMENTAL   PRINCIPLES   OF  CHEMISTRY 

case,  and  its  application  to  any  special  case  will  be  immediately 
evident. 

150.  Two  LIQUIDS.  —  According  to  what  we  have  just  said, 
the  statement  of  the  simplest  case  is  sufficient  for  the  explanation 
of  doubtful  cases  where  liquids  are  in  question.  The  simplest 
case  is  the  one  in  which  only  a  single  liquid  phase  can  exist,  what- 
ever the  relation  in  which  A  and  B  are  mixed.  In  other  words, 
whatever  compound  may  be  formed  is  soluble  in  all  proportions 
in  both  A  and  B. 

The  simple  laws  of  gaseous  solutions  do  not  hold  for  liquids, 
and  for  this  reason  the  criterion  we  made  use  of  for  gases,  deviation 
from  the  simple  gas  law,  is  no  longer  of  value.  This  means  that 
the  properties  of  liquid  solutions  can  no  longer  be  expressed  in 
a  diagram  by  straight  lines  connecting  the  values  of  the  properties 
of  the  constituents.  Their  place  will  be  taken  by  more  or  less 
curved  lines. 

In  one  important  point  we  will  find  agreement  with  the  simpler 
case.  Continuous  variation  in  the  proportion  of  A  and  B  leads  to 
a  definite  value  at  which  neither  A  nor  B  is  present  in  excess,  and 
at  this  point  the  whole  liquid  consists  of  the  pure  substance  AB. 
If  therefore  we  investigate  a  sufficient  number  of  systems  lying 
near  together  and  containing  A  and  B  in  varying  proportions,  we 
will  find  them,  in  general,  behaving  like  solutions  when  they  are 
distilled,  frozen,  or  allowed  to  crystallize.  The  system  which  con- 
tains the  two  constituents  in  the  relation  of  their  combining  weights 
will  be  the  only  one  showing  the  properties  of  a  pure  substance. 
It  will  be  a  matter  of  chance  if  we  find  among  the  various  mixtures 
one  which  corresponds  to  the  ratio  of  the  combining  weights.  But 
those  solutions  which  have  composition  most  nearly  corresponding 
to  this  ratio  will  contain  a  larger  proportion  of  the  pure  substance 
AB  than  those  lying  further  away,  and  in  this  sense  the  behaviour 
of  the  solution  approaches  that  of  the  pure  substance.  The  tem- 
perature at  which  the  change  into  another  state  takes  place  remains 
within  narrower  and  narrower  limits  as  the  proportions  approach 


ELEMENTS   AND  COMPOUNDS  229 

that  of  the  pure  substance  AB.  The  investigation  can  therefore 
be  begun  on  mixtures  lying  far  apart,  and  narrower  limits  of  com- 
position are  afterwards  to  be  chosen  between  those  mixtures  which 
show  the  most  constant  boiling  or  freezing  points,  until  the  pro- 
portion is  found  which  corresponds  to  a  hylotropic  transformation. 

This  general  method  presupposes  that  the  limit  of  stability  of 
the  substances  under  investigation  is  not  exceeded  in  either  direc- 
tion by  the  temperature  differences  maintained  during  distillation 
or  freezing.  The  question  whether  or  not  the  decision  can  be 
reached  under  constant  conditions  is  therefore  of  theoretical  im- 
portance, and  the  answer  to  this  question  is  an  affirmative  one. 

At  the  point  corresponding  to  the  ratio  of  the  combining  weights 
two  wholly  different  liquids  are  present  in  contact  with  each  other. 
We  should  therefore  not  expect  the  properties  of  the  liquids  to 
show  continuous  change  as  we  pass  through  this  point.  If  we  plot, 
as  in  Fig.  57,  the  value  of  any  property  —  volume,  for  example  — 
as  function  of  the  composition  with  respect  to  A  and  B,  the  line 
between  A  and  the  pure  compound  AB  will  not  in  this  case  be 
straight,  nor  will  the  line  between  AB  and  B.  These  two  lines  will 
however  be  continuous  over  their  whole  course.  They  will  cut 
each  other  at  a  finite  angle,  at  a  point  ab,  whatever  their  course 
may  have  been  on  either  side  of  this  point.  The  nature  of  the 
substances  A  and  B  and  the  nature  of  the  properties  investigated 
will  together  determine  what  this  angle  is.  If  in  any  case  the 
angle  is  so  small  that  it  cannot  be  recognised  with  certainty,  we 
may  turn  to  the  investigation  of  some  other  property  with  the 
hope  of  finding  an  angle  great  enough  to  place  the  proof  of  its 
existence  beyond  the  possible  errors  of  experiment.  The  problem 
is  therefore,  in  general,  possible  of  solution. 

The  general  form  of  a  diagram  which  is  to  indicate  the  formation 
of  a  chemical  compound  from  liquid  constituents  which  form  a 
solution  with  one  another  will  be  like  acb  of  Fig.  56,  properties 
being  plotted  against  composition,  as  in  this  diagram.  In  the 
present  case  more  or  less  curved  lines  take  the  place  of  the  straight 


230  FUNDAMENTAL  PRINCIPLES  OF  CHEMISTRY 

lines  of  Fig.  56  between  the  points  representing  the  properties  of 
the  pure  substances  (the  constituents)  and  the  compound.  A 
very  large  number  of  curve-forms  result,  and  some  of  these  are 


FIG.  58. 

shown  in  Fig.  58.     To  the  forms  shown  here  we  must  add  also 
their  opposites,  those  curving  upwards  instead  of  downwards. 

Conditions  are  most  favourable  for  the  investigation  when  the 
property  of  the  compound  lies  beyond  any  value  which  it  has  in 
the  constituents.  Under  these  circumstances  we  will  find  a  maxi- 
mum or  minimum  value  for  the  property  in  question  at  a  point 
corresponding  to  the  composition  of  the  compound.  This  charac- 


ELEMENTS  AND   COMPOUNDS  231 

teristic  is  more  and  more  evident  the  greater  the  difference  between 
the  average  value  for  the  constituents  and  the  actual  value  of  the 
property  in  the  compound.  This  will  be  immediately  evident  from 
a  consideration  of  Fig.  59.  If  the  difference  just  mentioned  is 


FIG.  59. 


slight,  the  curvature  of  the  lines  may  be  such  that  a  maximum  or 
minimum  appears  at  a  point  near,  but  not  exactly  that  correspond- 
ing to  the  proportions  of  the  compound,  as  shown  in  Fig.  60. 


FIG.  60. 


This  reasoning  is  true  only  under  the  assumption  that  the  com- 
pound AB  forms  completely  when  its  constituents  are  brought 
together  in  the  proper  proportion.  We  have  already  found  cases 


232 


FUNDAMENTAL   PRINCIPLES  OF  CHEMISTRY 


among  gases  where  curved  lines  took  the  place  of  straight  ones  and 
rounded  corners  replaced  sharp  angles.  It  has  already  been  shown 
that  the  explanation  of  these  cases  lies  in  the  fact  that  the  constitu- 
ents do  not  combine  completely  to  form  a  compound,  even  when 
they  are  present  in  the  proper  proportion.  A  so-called  homogene- 
ous equilibrium  exists  in  these  cases  between  the  three  substances, 
constituents  A  and  B  and  compound  AB,  which  depends  upon 
pressure,  temperature,  and  the  proportion  in  which  the  constituents 
are  present.  The  same  result  can  occur  between  liquid  solutions 
which  form  a  compound.  It  is  precisely  in  these  cases,  where  the 


FIG.  61. 

properties  of  the  compound  are  not  very  different  from  the  average 
value  of  the  properties  of  the  constituents,  that  such  incomplete 
reactions  are  most  usual.  Such  cases  are  doubly  indefinite,  and  the 
problems  involved  are  in  many  cases  still  beyond  our  present 
knowledge.  It  has  often  been  assumed  that  when  the  value  of 
the  property  passes  through  a  maximum  or  minimum,  as  a  series 
of  solutions  in  all  proportions  is  examined,  the  point  so  indicated 
determines  a  chemical  compound.  It  will  be  evident  from  Fig.  61 
that  when  the  property  line  is  not  straight  a  maximum  or  minimum 


ELEMENTS   AND  COMPOUNDS  233 

must  appear  in  every  case  where  the  values  of  the  property  are  the 
same  for  A  and  B,  and  that  such  a  maximum  or  minimum  becomes 
more  and  more  possible  as  the  difference  in  the  value  of  the  prop- 
erty for  A  and  B  becomes  less.  The  position  of  a  chemical  com- 


FIG.  62. 

pound  can  be  determined  much  more  certainly  by  finding  the 
maximum  deviation  of  the  property  from  the  average  value  of  the 
two  constituents,  as  shown  in  Fig.  62.  Even  this  method  cannot  at 
present  be  applied  with  certainty. 

151.  Two  SOLIDS.  —  The  question  just  considered  has  no  appli- 
cation to  solids,  for  here  a  phase  change  takes  places  generally  at 
the  point  where  the  proportion  of  the  constituents  corresponds  to 
the  value  of  the  constant  proportion  of  a  newly  formed  compound. 

152.  ANALYTICAL  METHODS.  —  The  following  question  will  now 
be  considered:   How  can  we  determine  with  certainty  the  fact 
that  a  pure  substance  has  exceeded  its  region  of  stability?    The 
consequence  of  such  a  change  will  be  the  transformation  of  the 
substance  in  question  into  a  solution  or  a  mixture.    Among  gases 
we  have  only  the  first  case  to  consider,  since  they  do  not  form 
mixtures,  but  among  solids  the  second  case  is  typical.    Either  case 
may  apply  to  liquids.     The  limit  of  stability  can  be  exceeded  by 
subjecting  the  substance  to  changes  of  pressure  and  temperature. 


234  FUNDAMENTAL   PRINCIPLES  OF  CHEMISTRY 

In  case  a  mixture  is  the  result  of  the  change,  it  can  be  immedi- 
ately recognised  by  the  characteristics  given  in  Sec.  39.  A  change 
in  optical  properties  is  easiest  to  recognise.  A  substance  origi- 
nally transparent  may  become  milky;  changes  in  colour  or  other 
changes  in  appearance  may  take  place.  There  are,  of  course, 
cases  where  examination  with  the  eye  alone  is  insufficient;  the 
microscope  is  often  of  great  assistance,  especially  when  the  change 
involves  the  appearance  and  disappearance  of  solids.  Recognition 
of  the  change  is  therefore,  in  general,  possible  whenever  a  mixture 
results  from  overstepping  the  limit  of  stability. 

If  a  solution  is  produced  the  following  general  relations  come 
into  consideration.  A  pure  substance  does  riot  change  suddenly 
and  completely  into  a  solution;  the  process  is  a  gradual  one,  and 
not  like  the  transformation  of  one  state  into  another.  It  is,  in  gen- 
eral, impossible  to  find  a  definite  point  separating  the  region  of  the 
pure  substance  from  that  of  the  solution  which  forms  from  it.  It 
is  usually  only  possible  to  determine  approximately  a  point  where 
the  p!roof  that  a  chemical  process  has  taken  place  can  be  given 
with  certainty.  This  point  depends  upon  the  accuracy  of  the  ana- 
lytic means,  and  it  might  even  be  stated  on  general  grounds  that 
there  is  no  such  thing  as'  an  absolutely  pure  substance.  This 
contention  will  have  its  basis  in  the  fact  that  there  is  no  point  of 
discontinuity  which  separates  the  region  of  a  so-called  pure  sub- 
stance from  that  corresponding  to  the  solution  formed  from  it. 
Practically,  however,  the  differentiation  of  a  region  of  stability 
from  one  of  instability  has  importance.  The  region  in  which 
experimental  proof  of  a  change  is  impossible  is  usually  evidently 
different  from  the  region  in  which  analysis  can  give  positive  re- 
sults. In  other  words,  there  are  very  large  regions  in  which  the 
amount  of  decomposition  is  exceedingly  minutej  and  the  transition 
to  finite  values  begins  at  a  place  where  comparatively  small  changes 
in  temperature  and  pressure  correspond  to  measurable  changes. 

Such  continuity  in  transformation  and  the  presence  of  homo- 
geneous equilibria  prevent  the  application  of  the  criteria  of  Sections 


ELEMENTS  AND  COMPOUNDS  235 

145  et  seq.  Phase  diagrams  are  nearly  useless,  for  we  have  repeat- 
edly seen  that  the  finite  angles  which  appear  as  we  go  from  one 
part  of  the  diagram  to  another,  and  which  correspond  to  the 
formation  of  new  substances,  are  all  rounded  off  whenever  a 
homogeneous  equilibrium  results.  The  value  of  such  diagrams 
as  characteristics  of  new  substances  is  therefore  more  or  less 
eliminated. 

We  must  find  other  characteristics  if  there  are  any.  The  material 
at  hand  can  be  again  laid  out  from  the  standpoint  of  states.  We 
must  then  consider  the  transformation  of  pure  gases,  liquids,  and 
solids  into  corresponding  solutions;  the  solutions,  however,  in  this 
case  being  invariably  in  the  same  state  as  the  pure  substance.  We 
shall  not  consider  solutions  of  solids,  but  only  those  of  gases  and 
liquids. 

153.  GASES.  —  Whenever  a  gaseous  solution  is  formed  from 
a  pure  gas,  the  experimental  recognition  of  the  change  can  usually 
be  based  upon  the  fact  that  the  simple  gas  laws  no  longer  hold. 
Let  us  assume,  for  example,  that  the  gas  in  question  is  transformed 
into  a  gaseous  solution  by  heating  it,  and  that  the  newly  formed 
gases  possess  a  volume  different  from  that  of  the  original  gas.  As 
long  as  the  temperature  lies  within  the  region  of  stability  the  gas 
follows  Boyle's  Law  and  Gay-Lussac's  Law.  When  the  temperature 
reaches  the  region  of  decomposition,  the  coefficient  of  expansion 
of  the  gas  will  become  greater  than  %\-$  if  the  product  of  decom- 
position occupies  a  greater  volume  than  the  original  gas  (and  vice 
versa).  In  the  same  case  deviations  from  Boyle's  Law  will  appear, 
and  the  gas  will  show  a  greater  or  less  compressibility  than  that 
indicated  by  the  law.  Whether  a  rise  of  temperature  causes  the 
gas  to  enter  a  region  of  decomposition  depends  upon  whether  it 
takes  in  or  gives  out  heat  or  entropy  during  the  decomposition. 
According  to  our  general  definition  of  equilibrium  a  system  reacts 
to  a  forced  change  in  such  a  way  that  the  result  of  the  force  is 
diminished  (see  Sec.  67).  If  a  gas  can  change  its  equilibrium  by 
a  chemical  reaction,  the  addition  of  heat  (a  rise  of  temperature) 


236  FUNDAMENTAL  PRINCIPLES  OF  CHEMISTRY 

will  bring  about  a  reaction  of  such  a  nature  as  to  diminish  the 
consequences,  that  is,  in  this  case,  to  diminish  the  rise  of  tempera- 
ture. If  the  decomposition  is  accompanied  by  an  absorption  of 
heat,  this  absorption  will  take  place.  If  the  reverse  is  true,  and 
the  decomposition  is  accompanied  by  the  development  of  heat, 
the  gas  will  become  more  stable  at  higher  temperatures.  The 
second  case  is  far  the  rarer  of  the  two  under  ordinary  conditions, 
but  there  is  sufficient  ground  for  concluding  that  cases  of  this  kind 
become  more  numerous  as  temperature  is  carried  higher  and 
higher. 

Pressure  acts  in  a  similar  way.  If  the  transformation  into  a 
solution  is  accompanied  with  an  increase  of  volume,  the  decomposi- 
tion under  diminishing  pressure  will  go  further  and  further  as  the 
volume  is  made  greater.  The  decrease  in  pressure  is  partly  com- 
pensated by  the  formation  of  a  solution  which  occupies  a  compara- 
tively greater  volume.  When  the  volume  is  forcibly  decreased, 
and  the  pressure  is  found  to  be  lower  than  it  would  be  for  a  pure 
substance  according  to  Boyle's  Law,  this  result  corresponds  to  a 
chemical  process  opposite  in  nature  to  the  one  just  described. 
Beside  this  characteristic  of  the  resulting  gaseous  solution  we  can 
also  make  use  of  those  characteristics  described  in  Sections  84  et  seq. 
Partial  solution  or  partial  separation  of  a  part  of  the  gas  solution 
(by  diffusion,  for  example,  as  in  Sec.  84)  will  result  in  a  residue 
exhibiting  properties  different  from  those  of  the  original  gas.  In 
this  case,  however,  we  are  confronted  by  a  new  and  important 
factor  which  does  not  prevent  the  final  decision,  but  which  makes 
quantitative  determination  impossible.  As  one  of  the  constituents  is 
removed  chemical  reaction  immediately  takes  place  in  the  residue. 
The  escaping  constituent  is,  in  general,  partially  replaced,  and  this 
is  the  result  of  the  principle  which  has  just  been  expressed  and 
applied.  Wholly  false  conclusions  as  to  the  amount  of  the  escap- 
ing substance  which  was  present  in  the  original  gas  may  be  drawn 
if  these  facts  are  not  kept  in  mind.  Consider  the  case  of  a  process 
by  which  only  one  of  the  constituents  of  the  solution  is  withdrawn. 


ELEMENTS  AND  COMPOUNDS  237 

According  to  our  general  rule,  this  substance  must  be  continually 
formed  as  it  is  withdrawn.  If  we  then  took  away  all  of  this  sub- 
stance that  was  formed  we  would  have  separated  an  amount 
which  was  never  really  present  in  the  original  mixture,  although  it 
was  potentially  there.  By  potentially  we  mean  in  this  case  the 
entire  amount  which  could  be  formed  from  the  substances  present, 
provided  all  hindrance  which  might  prevent  the  completeness  of 
the  reaction  in  question  is  removed.  This  conclusion  is  an  impor- 
tant one  and  finds  application  in  many  other  cases  outside  of  gas 
reactions.  A  careful  review  of  the  facts  in  connection  with  this 
principle  will  show  that  it  holds  for  all  homogeneous  equilibria 
in  gases  and  in  liquids  of  all  kinds. 

154.  LIQUIDS.  —  We  possess  no  general  quantitative  laws  for 
liquids  similar  to  those  for  gases,  and  we  can  therefore  place  no 
dependence  on  any  such  aids  for  differentiating  between  pure 
substances  and  solutions  in  the  case  of  liquids.  At  the  same  time 
the  conditions  here  also  exclude  the  application  of  the  angles  at 
the  points  of  contact  of  property  lines  in  the  phase  diagrams,  for 
all  these  points  are  rounded  off  by  the  existing  homogeneous  equi- 
libria. All  sharp  differences  between  solution  and  pure  substance 
are  absent  as  long  as  we  are  dealing  only  with  the  properties  of 
the  liquid  phase,  and  we  can  therefore  never  decide  by  observa- 
tions of  this  kind  whether  and  where  a  pure  substance  leaves  its 
region  of  stability. 

Our  process  for  the  partial  separation  can,  however,  be  applied, 
and  even  this  assumes  the  formation  of  a  new  phase  of  some  kind. 
Whether  or  not  a  liquid  is  stable  can,  in  general,  be  easily  decided 
by  distillation.  By  this  process  the  more  volatile  portions  of  the 
solution  will  be-  the  first  to  escape,  and  the  composition  of  the 
vapour  will,  in  general,  be  different  from  that  of  the  residue.  In 
the  case  of  a  singular  solution  this  does  not  hold,  for  here  the 
distillation  will  be  hylotropic.  A  change  of  pressure  will  be  of 
assistance  in  this  case,  for  with  such  a  change  in  pressure  the 
solution  will  lose  its  singular  properties. 


238 


FUNDAMENTAL  PRINCIPLES   OF  CHEMISTRY 


A  partial  freezing  out  is  also  insufficient,  even  though  a  partial 
separation  may  apparently  be  produced.  In  this  case  it  is  neces- 
sary to  inquire  which  constituent  of  the  solution  is  the  first  to 
separate.  If  it  is  the  original  substance,  this  will  keep  on  form- 
ing from  its  components  in  the  liquid  according  to  the  principles 
just  explained.  The  whole  liquid  will  therefore  appear  hylotropic 
during  freezing  and  the  presence  of  a  solution  remains  undeter- 
mined. If,  on  the  other  hand,  one  of  the  constituents  separates 
first,  the  presence  of  a  solution  will  be  evident.  Brief  considera- 
tion of  the  diagram  representing  what  takes  place  during  freezing 
shows  that  in  this  case  the  compound  is  the  first  to  separate.  To 
make  this  clear  let  us  consider  the  corresponding  diagram,  Fig.  63, 


u 


FIG.  63. 

in  which  the  rounding  off  of  the  peak  in  the  centre  is  already  shown 
as  a  result  of  the  homogeneous  equilibrium.  The  solution  has 
been  formed  by  the  decomposition  of  the  compound.  Its  com- 
position is  therefore  that  of  the  compound,  and  the  course  of  the 
experiment,  which  consists  in  cooling  the  liquid,  will  be  repre- 
sented along  the  perpendicular  uu.  The  melting  line  must  neces- 
sarily be  crossed  at  the  peak.  From  this  it  is  evidently  impossible 
that  one  of  the  constituents  should  separate  as  a  solid,  and  under 
all  circumstances  the  compound  will  separate  in  the  solid  condi- 
tion. It  will  be  seen  that,  in  general,  the  determination  of  one  of 


ELEMENTS  AND   COMPOUNDS  239 

the  boundaries  of  the  region  of  stability  for  liquids  offers  difficul- 
ties and  is  by  no  means  always  possible. 

Solid  substances  can  only  produce  mixtures  when  they  exceed 
their  limit  of  stability,  and  these  mixtures  are  theoretically  always 
recognisable. 

155.  TRIPLE  SYSTEMS.  —  Up  to  this  point  we  have  only  con- 
sidered systems  which  could  be  produced  from  two  pure  substances. 
It  will  be  evident  from  the  great  number  of  possibilities  which  we 
have  found  that  a  very  much  larger  number  of  individual  cases 
are  to  be  expected  among  triple  systems.  It  will  be  impossible  here 
to  develop  even  a  general  idea  of  the  possibilities,  and  we  will  con- 
fine our  discussion  to  an  especially  important  group,  —  one  which 
is  experimentally  most  often  met  with.  This  group  comprises  re- 
actions between  dilute  solutions  having  a  common  solvent.  The 
reason  for  the  special  advantage  of  this  group  is  to  be  found  in 
the  following  circumstances:  Firstly,  dilute  solutions  occur  very 
frequently  in  nature.  Substances  are  very  seldom  formed  alone; 
•as  soon  as  several  come  in  contact  they  form  solutions,  and  when 
the  mutual  solubility  is  limited  these  solutions  will  be  dilute. 
Secondly,  dissolved  substances  react  with  one  another  much 
more  easily  than  solids.  If  chemical  processes  are  to  be  brought 
about,  it  is  always  best  first  of  all  to  bring  the  solids  into  solution. 

Suppose  we  have  three  substances  A,  B,  and  C  of  such  a  nature 
that  A  and  B  are  soluble  in  C.  Let  us  consider  what  happens 
when  a  dilute  solution  of  A  in  C  is  allowed  to  react  with  a  dilute 
solution  of  B  in  C.  If  both  A  and  B  are  far  removed  from  a  con- 
dition of  saturation  in  C,  and  when  A  and  B  do  not  combine  to 
form -a  new  substance,  the  resulting  substance  will  be  a  homo- 
geneous solution.  It  is  of  course  possible  that  the  solubility  of 
one  or  the  other  constituent  will  be  so  greatly  reduced  by  combining 
the  two  solutions  that  the  corresponding  substance  will  separate 
as  a  new  phase.  This  can,  however,  only  take  place  when  one 
or  the  other  of  the  two  solutions  is  near  saturation,  and  this  we 
have  excluded  in  our  assumption.  Such  a  case  is  furthermore 


240  FUNDAMENTAL  PRINCIPLES  OF  CHEMISTRY 

so  easy  to  recognise  that  we  can  for  the  future  leave  it  out  of 
consideration. 

If  new  phases  appear  when  two  dilute  solutions  are  brought 
together,  it  is  safe  to  conclude  that  a  new  substance  has  been 
formed  by  the  interaction  of  A  and  B.  If  new  phases  do  not  appear, 
we  must  not  however  conclude  that  a  new  substance  has  not  been 
formed.  The  new  substance  may  be  so  soluble  in  C  that  no  new 
phase  can  form.  In  a  case  of  this  kind  we  must  bring  to  our  aid 
other  means  for  recognising  a  chemical  process.  The  most  general 
of  these  is  in  this  case  also  a  change  of  the  total  energy  of  the 
system,  which  may  be  evidenced  by  the  evolution  or  absorption 
of  heat.  Two  possibilities  may  come  in  question,  —  liquid  solutions 
and  gaseous  solutions.  We  shall  consider  exclusively  the  first  of 
these,  for  this  is  the  one  of  the  most  practical  importance.  We  have 
therefore  to  investigate  phase  changes  in  dilute  liquid  solutions. 

It  should  be  mentioned  at  this  point  that  when  a  substance  enters 
the  condition  of  a  dilute  liquid  solution  it  follows  a  set  of  simple 
laws,  just  as  it  does  after  it  has  entered  the  gaseous  state.  A  little' 
later  we  shall  see  that  the  similarity  goes  so  far  that  an  equation 
of  condition  holds  for  dissolved  substances  which  corresponds 
exactly  to  the  gas  law.  At  this  point  we  shall  make  no  application 
of  this  relationship.  For  the  present  we  are  interested  in  a  general 
explanation  of  the  formation  of  the  phases  and  not  in  quantita- 
tive relations  within  a  phase. 

156.  INDIVIDUAL  CASES.  —  Three  different  cases  are  possible 
under  our  assumptions:  either  a  gas,  another  liquid,  or  a  solid 
substance  may  separate  from  the  liquid  phase.  All  three  of  these 
cases  are  known,  and  either  of  them  determines  the  conclusion 
that  under  these  circumstances  a  new  substance  has  been  formed. 
This  new  substance  may  be  a  compound  of  A  and  B,  but  it  is 
equally  possible  that  the  new  substance  contains  some  of  the  sol- 
vent C,  or  that  the  new  substance  does  not  contain  the  sum  of  the 
elements  of  A  and  B,  but  only  part  of  them.  In  the  latter  case  one 
or  more  new  substances  remain  in  the  solution,  these  new  sub- 


ELEMENTS  AND  COMPOUNDS  241 

Stances  being  such  as  have  been  formed  by  the  reaction  together 
with  the  one  which  separated  in  the  form  of  a  new  phase. 

Reactions  in  solutions  have  one  thing  at  least  in  common  with 
those  in  gases.  The  formation  of  a  new  substance  can  always  be 
recognised  with  certainty  when  a  new  phase  belonging  to  another 
state  results  from  the  reaction.  The  possibility  of  recognising  a 
new  phase  which  separates  in  any  of  the  three  states  gives  to  solu- 
tions an  advantage  over  gases  in  the  proof  of  chemical  processes. 
For  in  the  case  of  gases  a  new  gaseous  substance  would  not  ap- 
pear as  a  new  phase.  For  this  reason,  and  also  because  it  is  much 
easier  to  handle  liquids  than  gases,  solutions  possess  their  great 
practical  importance  in  experimental  chemistry. 

157.  THE  EVOLUTION  OF  A  GAS. — Let  us  consider  the  case 
in  which  a  reaction  between  the  two  solutions  of  A  in  C  and  B  in  C 
results  in  the  formation  of  a  gas.  It  makes  no  difference  as  far 
as  the  general  reasoning  is  concerned  whether  this  gas  has  the 
composition  AB  or  is  formed  in  some  other  way  from  the  two  sub- 
stances and  the  solvent,  and  we  shall  therefore  riot  consider  this 
point  further.  Suppose  we  add  a  very  small  amount  of  A  (we 
shall  use  this  expression  for  the  sake  of  brevity  in  the  future  dis- 
cussion in  place  of  saying  "  solution  of  A")  to  a  finite  amount  of 
B ;  no  evolution  of  gas  is  to  be  expected.  All  gases  are  soluble  in 
all  liquids,  and  the  newly  formed  gas  will  therefore  be  soluble  in 
the  solution.  We  have  also  assumed  that  the  solutions  are  dilute. 
The  solubility  of  the  new  gas  will  therefore  not  be  very  different 
from  its  solubility  in  the  pure  solvent  C.  When  further  addition 
of  A  has  resulted  in  the  formation  of  so  large  an  amount  of  gas 
that  saturation  is  reached,  gas  may  be  evolved  on  further  additions. 
This  does  not,  however,  necessarily  take  place.  Supersaturation 
will  occur,  since  this  takes  place  easily  in  solutions  of  gases  in 
liquids.  The  condition  of  supersaturation  can  be  released  by  any 
foreign  gas,  and  it  is  therefore  easy  to  recognise.  It  is  only  neces- 
sary to  shake  a  sample  of  the  mixed  solutions  with  a  measured 
volume  of  any  indifferent  gas,  atmospheric  air,  for  example,  and 
16 


242  FUNDAMENTAL  PRINCIPLES   OF  CHEMISTRY 

then  to  measure  the  gas  volume  again.  An  increase  of  volume 
will  indicate  the  presence  of  a  supersaturated  solution  of  gas.* 

Assuming  that  no  pains  have  been  taken  to  avoid  supersatura- 
tion,  further  additions  of  A  will,  in  general,  finally  result  in  reach- 
ing the  labile  condition,  where  the  evolution  of  gas  begins  of  its 
own  accord.  As  A  is  further  increased,  the  amount  of  gas  pro- 
duced will  increase  until  all  of  B  has  been  used  up.  From  this 
point  on  the  further  evolution  of  gas  ceases. 

Measurement  of  the  amount  of  gas  produced  during  the  opera- 
tion of  gradually  adding  A  to  E  enables  us  to  determine  the  pro- 
portion in  which  A  and  B  combine,  or  it  may  be  the  proportion 
in  which  they  act  on  one  another  in  some  other  way.  Precisely 
similar  conditions  prevail  when  the  process  is  carried  out  in  the 
inverse  way  by  gradually  permitting  an  increasing  amount  of  B 
to  act  upon  A. 

158.  LIQUID  SEPARATION.  What  we  have  just  said  can  be 
repeated  almost  word  for  word  if  we  wish  to  describe  what  takes 
place  when  a  liquid  which  separates  as  a  new  phase  is  formed  by 
the  interaction  of  A  and  B  (and  of  C  also).  The  limit  of  satura- 
tion for  the  new  substance  must  be  reached  before  this  can  appear 
as  a  separate  phase.  It  is  a  matter  of  experience  that  in  the  case 
of  solutions  of  liquids  in  liquids  supersatu ration  appears  only 
with  difficulty  and  within  very  narrow  limits,  so  that  the  com- 
plexity introduced  by  its  appearance  is  absent  in  this  case.  On 
the  other  hand,  there  is  no  general  means  of  releasing  supersat- 
uration  similar  to  the  one  afforded  by  the  indifferent  gas  in  the 
previous  paragraph. 

Another  thing  should  be  mentioned  here,  and  that  is  the  usually 
occurring  case  of  local  precipitation.  As  A  is  added  to  B  it  will 

*  It  must  of  course  be  kept  in  mind  that  the  liquid  will  also  dissolve  the  in- 
different gas  according  to  its  solubility,  and  also  that  the  vapour  of  the  liquid 
will  increase  the  gas  volume  in  proportion  to  the  vapour  pressure  of  the 
solution.  There  is,  however,  no  difficulty  in  excluding  these  effects  or  cal- 
culating them,  and  we  shall  therefore  assume  that  they  have  been  taken  into 
consideration. 


ELEMENTS   AND   COMPOUNDS  243 

be  noticed  that  at  the  moment  when  the  two  solutions  touch,  the 
separation  of  a  new  phase  is  indicated  by  a  milkiness  in  the  liquid. 
This  disappears  when  the  liquid  is  stirred  and  the  solution  becomes 
clear  again.  In  the  neighbourhood  of  the  drop  the  proportion  of 
A  to  B  is  at  first  much  greater  than  it  would  be  if  the  two  liquids 
were  intimately  mixed.  The  effect  which  is  later  to  appear  every- 
where is  seen  first  at  this  place.  Later  the  local  proportion  will 
be  attained  everywhere  by  the  addition  of  a  larger  amount  of  A. 
When  the  general  proportion  is  restored  by  mechanically  stirring, 
the  new  phase  which  separates  locally  is  again  dissolved  and  the 
liquid  becomes  clear. 

The  combining  proportion  of  A  to  B  can  be  theoretically  de- 
termined in  this  case  also,  for  the  separation  of  the  new  phase 
ceases  when  this  proportion  is  reached.  It  is,  however,  experi- 
mentally very  much  more  difficult  to  determine  in  this  case,  for  the 
new  liquid  usually  forms  a  milky  mixture,  an  emulsion,  in  which 
it  is  difficult  to  recognise  an  increased  milkiness  as  more  of  A  is 
added.  It  is  however  possible  to  separate  the  phases  by  letting 
the  liquid  stand  or  by  means  of  a  centrifuge,  and  then  to  recognise 
further  precipitation  of  the  new  phase.  The  solution  of  this  prob- 
lem has  been  indicated,  and  we  need  not  follow  the  technical 
methods  any  further. 

159.  SOLID  SEPARATION.  —  By  far  the  greatest  number  of  practi- 
cally important  cases  depend  upon  the  separation  of  a  new  phase 
in  the  solid  form.  In  this  case  it  is  called  a  precipitate,  for  the 
solid  phase  almost  always  has  a  greater  density  than  the  liquid 
and  sinks  to  the  bottom  of  the  vessel.  The  general  phenomena, 
which  occur  as  one  solution  is  gradually  added  to  the  other,  are  in 
no  way  different  from  those  described  in  the  case  of  gases  or  liquid 
phases.  In  this  case  also  there  is  a  homogeneous  region  at  each 
end  of  the  series  of  mixtures  which  corresponds  to  the  solubility 
of  the  new  phase  in  the  solvent  (as  influenced  by  the  dissolved 
substances).  Between  these  two  regions  there  is  a  two-phase 
region  in  which  the  precipitate  exists  in  the  presence  of  the  solution. 


244  FUNDAMENTAL   PRINCIPLES  OF  CHEMISTRY 

Each  constituent  acts  upon  the  other  to  form  the  precipitate  until 
the  point  is  reached  which  determines  the  ratio  of  the  combining 
weights.  When  this  point  has  been  reached  neither  A  nor  B 
causes  a  precipitate  in  the  liquid,  while  in  all  other  proportions  in 
the  two-phase  region  either  A  or  B  produces  one. 

Supersatu ration  is  very  frequent  among  these  cases.  There  are 
in  fact  cases  where,  although  a  solid  phase  is  possible,  it  never 
appears  of  its  own  accord  whatever  the  proportion  in  which  the 
solutions  are  mixed.  It  is  usually  possible  to  pass  the  metastable 
limit  by  increasing  the  concentration,  and  if  particles  of  the  solid 
phase  can  be  obtained,  it  is  possible  to  prevent  supersaturation 
from  the  first. 

In  every  case,  whatever  the  state  of  the  second  phase  may  be, 
we  have  to  deal  with  systems  containing  three  constituents  and 
two  phases,  and  we  have  therefore  three  degrees  of  freedom. 
Pressure  and  temperature  being  determined,  one  degree  of  freedom 
remains.  This  means  that  if  we  fix  the  concentration  of  A  that 
of  B  is  no  longer  free  but  must  possess  a  definite  value,  and  vice 
versa.  Only  one  of  the  two  proportions  A  to  C  and  B  to  C  is  free, 
the  third  proportion  A  to  B  is  determined  by  the  two  first  and  is 
therefore  not  independent.  The  above  only  holds  in  case  the 
new  phase  has  appeared,  and  in  those  regions  in  which  the  new 
phase  has  not  yet  been  formed  one  more  degree  of  freedom  remains. 
The  solution  may  have  any  composition  within  the  corresponding 
limits. 

160.  THE  SOLUTION  REMAINS  HOMOGENEOUS.  —  In  conclu- 
sion let  us  examine  the  case  in  which  no  new  phase  appears  within 
all  the  possible  proportions  in  which  the  two  solutions  can  be 
mixed.  Whether  or  not  a  new  substance  has  been  produced  by 
the  interaction  of  A  and  B  (with  or  without  the  aid  of  C)  may  be 
determined  by  reasoning  similar  to  that  of  Sec.  146.  In  that  sec- 
tion we  considered  the  case  where  two  gases  form  a  homogeneous 
solution. 

The  energy  relations  are  directly  applicable  as  in  Sec.   148. 


ELEMENTS  AND   COMPOUNDS  245 

When  solutions  are  formed  from  liquid  constituents  there  is,  in 
general,  an  energy  change,  even  though  we  have  no  other  ground 
for  the  assumption  that  a  new  substance  has  been  formed.  The 
similarity  of  dilute  solutions  and  gases  is  marked  especially  by  the 
fact  that  these  energy  changes,  which  do  not  correspond  to  the 
appearance  of  a  new  substance,  become  less  and  less  as  the  solu- 
tions are  made  more  and  more  dilute.  This  is  in  agreement  with 
the  behaviour  of  gases  which  dissolve  one  another  without  change 
as  long  as  no  chemical  reaction  takes  place  between  them.  If  a 
chemical  change  takes  place  the  energy  change,  due  to  the  chemical 
process,  appears  completely  in  the  heat  change  produced  when 
dilute  solutions  are  mixed. 

Any  other  specific  property  beside  energy  change  would  serve 
as  well,  provided  it  shows  a  change  as  compared  with  the  average 
value  of  the  corresponding  mixture  or  solution.  Suppose,  for 
example,  that  A  is  coloured,  while  the  newly  formed  compound  is 
colourless.  Then  as  A  is  added  to  B  we  should  see  the  colour  of 
A  disappear  until  the  relation  of  the  combining  weights  is  reached. 
In  general  such  a  property  will  exhibit  changes  like  those  indicated 
in  Fig.  57.  Here  we  find  the  diagram  to  consist  of  two  straight 
lines  cutting  one  another  at  a  point  which  represents  the  ratio  of 
the  combining  weights. 

It  should  be  mentioned  that  these  simple  relations  do  not  hold 
in  some  cases.  In  place  of  the  sharp  angle  at  the  meeting  of  the 
two  lines  we  may  find  a  rounded  corner.  In  these  cases,  as  with 
the  gases,  it  is  possible  to  represent  the  observed  facts  by  assuming 
a  chemical  equilibrium  which  varies  with  changes  in  temperature 
and  concentration. 

The  relations  just  discussed  for  solutions  are  of  the  utmost  im- 
portance. They  are  of  use  in  the  recognition  of  substances  in 
their  solutions,  and  they  therefore  form  the  foundation  of  analyti- 
cal chemistry.  The  use  of  solutions  in  place  of  pure  substances 
is  largely  dependent  upon  the  fact  that  the  former  exhibit  simpler 
and  more  general  relations  than  the  corresponding  pure  substances, 


246  FUNDAMENTAL  PRINCIPLES   OF  CHEMISTRY 

and  this  is  especially  true  in  a  case  of  the  greatest  practical  im- 
portance. This  is  the  class  of  salts,  which  will  be  taken  up  in  a 
later  chapter  and  there  defined  and  characterized  as  far  as  their 
important  properties  are  concerned.  In  those  substances  which 
do  not  belong  to  the  salt  type,  and  especially  among  the  carbon 
compounds,  solutions  are  of  no  advantage,  and  in  these  cases  sub- 
stances are  used  and  recognised  in  their  pure  condition  rather  than 
in  solution. 


CHAPTER  VII 
THE   LAW  OF   COMBINING  WEIGHTS 

161.  THE  LAW  OF  CONSTANT  PROPORTIONS.  —  It  has  been 
shown  in  the  discussion  of  the  previous  chapter  that  new  substances 
are  produced  from  old  ones  in  two  ways.  The  first  of  these  ways 
is  to  bring  together  several  substances,  while  the  second  way  in- 
volves the  use  of  only  a  single  substance  brought  into  conditions 
of  such  a  nature  that  its  region  of  stability  is  exceeded.  In  both  of 
these  cases  the  new  pure  substances  frequently  appear  in  the  form 
of  solutions  and  not  in  the  pure  state.  The  question  how  constit- 
uents can  be  separated  in  a  pure  state  from  their  solutions  has 
already  been  taken  up.  We  may  therefore  assume  in  what  follows 
that  the  new  substances  which  are  formed  under  the  existing  con- 
ditions have  been  brought  into  the  pure  state  by  the  proper  opera- 
tions. The  law  of  constant  proportions  (Sec.  149)  deals  with 
the  amounts  by  weight  in  which  new  substances  are  produced  from 
those  already  present.  This  means  that  a  definite  relation  exists 
between  the  weights  of  the  original  substances  and  the  newly 
formed  products.  This  relation  varies  with  the  nature  of  the  sub- 
stances involved,  but  it  is  independent  of  pressure,  temperature, 
or  any  other  condition  existing  during  the  transformation.  The 
"  nature"  of  the  substances  involved  is  characterized  by  their 
properties,  and  substances  with  the  same  properties  are  to  be  con- 
sidered as  having  the  same  nature.  In  other  words,  the  relations  by 
weight  in  which  chemical  transformations  take  place  belong  to  the 
definite  and  specific  properties  by  which  substances  are  classified 
as  the  same  or  different. 

Suppose  we  have  two  substances,  A  and  B,  which  can  combine 

247 


248  FUNDAMENTAL   PRINCIPLES   OF  CHEMISTRY 

into  a  compound  AB,  the  original  substances  disappearing  and 
the  new  substance  AB  appearing  in  their  place.  The  law  which 
describes  this  case  states  that  when  these  two  substances  are 
brought  together  in  a  definite  proportion  a  new  pure  substance  is 
formed  which  is  neither  a  mixture  nor  a  solution.  The  same  rela- 
tion is  found  unchanged  whenever  a  pure  substance  possessing  the 
properties  of  the  substance  AB  is  transformed  or  decomposed  in 
any  way  into  the  two  substances  A  and  B.  This  second  principle 
can  be  derived  as  a  consequence  of  the  first  with  the  aid  of  the  law 
of  the  conservation  of  the  elements.  If  AB  could  be  decomposed 
in  such  a  way  as  to  give  the  elements  A  and  B  in  a  proportion  dif- 
ferent from  the  one  in  which  they  combined  to  form  AB,  we  would 
be  able  by  combining  A  and  B  and  then  decomposing  their  com- 
pound to  get  more  A  or  more  B  than  we  had  originally.  This 
is  contrary  to  the  law  of  the  conservation  of  the  elements. 

This  proof  assumes  that  A  and  B  are  elements,  but  it  can  also 
be  expanded  to  include  the  case  where  A  and  B  are  compounds. 
If  the  law  did  not  hold  we  would  be  able  to  obtain  an  excess  of  A 
or  B,  and  by  decomposing  this  into  its  elements  we  could  obtain 
an  excess  of  one  or  the  other.  It  may  be  said,  in  general,  that  every 
compound  shows  the  same  composition,  whether  it  is  synthesized 
from  its  elements  (or  from  compounds  made  up  of  them)  or  an- 
alyzed in  such  a  way  as  to  produce  them.  The  elements  in  a  com- 
pound are  present  in  a  definite  proportion  which  appears  in  both 
analysis  and  synthesis. 

The  law  of  constant  proportions  holds  only  for  pure  substances, 
it  therefore  holds  for  these  only  within  their  regions  of  stability, 
for  outside  of  these  regions  the  pure  substances  cannot  exist  as 
such.  Proof  that  this  proportion  is  independent  of  variations  of 
pressure  and  temperature  depends  on  the  assumption  that  the 
region  of  stability  is  not  exceeded. 

We  shall  see  later  that  the  condition  thus  assumed  is  a  funda- 
mental one,  and  that  furthermore  the  law  of  constant  proportions 
holds  for  all  pure  substances  whether  they  are  elements  or  not. 


THE   LAW  OF  COMBINING   WEIGHTS  249 

When  any  two  substances  form  a  new  substance  by  chemical  inter- 
action there  is  always  a  relation  by  weight  of  these  two  substances, 
and  in  this  relation  the  new  compound  appears  as  a  pure  substance 
and  not  as  a  solution.  Compound  substances  enter  into  further  com- 
binations as  a  whole  just  as  elements  do.  Whether  or  not  a  given 
substance  is  an  element  can  only  be  determined  by  an  investiga- 
tion throughout  the  whole  range  of  pressures,  temperatures,  etc. 
The  proof  that  it  does  not  change  into  a  solution  is  dependent  on 
the  development  of  the  technique  of  chemistry,  and  it  is  therefore 
evident  that  there  is  no  absolute  difference  between  simple  and 
compound  substances  as  long  as  any  part  of  the  whole  range  of 
temperature  and  pressure  has  not  been  explored  in  each  case.  All 
pure  substances  agree  further  in  their  power  to  combine  to  form 
more  complex  substances,  and  this  is  true  whether  they  have  been 
shown  to  be  compounds  or  are  still  classed  as  elements.  The  law 
just  explained  depends  upon  an  inestimable  number  of  observa- 
tions, and  we  shall  call  it  the  law  of  integral  reactions . 

162.  COMBINING  WEIGHTS.  —  Let  A,  B,  C,  D,  etc.,  be  elements 
which  can  combine  with  each  other.  Suppose  also  that  the  relation 
in  which  any  given  element,  A,  for  example,  combines  with  the 
others  has  been  determined.  We  have  then  determined  the  com- 
bining proportions  of  the  substances  AB,  AC,  AD,  etc.  If  we  take 
the  amount  of  A  which  was  used  for  each  of  these  syntheses  as  our 
unit,  then  the  amounts  of  B,  C,  D,  etc.,  which  combine  with  the 
unit  weight  of  A,  are  called  the  combining  weights  of  these  elements 
with  respect  to  A,  and  they  might  be  indicated  by  (B)A,  (C)A, 
(D)A,  etc. 

We  might  just  as  well  have  different  combining  weights  based 
upon  B,  i.  e.  the  weights  of  the  other  elements  which  would  com- 
bine with  the  unit  weight  of  B  to  form  the  compounds  BA,  BC,  BD, 
etc.  This  would  give  us  a  system  of  combining  weights  based  upon 
B,  and  we  will  designate  them  with  (A)B,  (C)s,  (D)s,  etc. 

Let  us  now  assert  that  (B)A  x  (A)a  =  1.  Expressed  in  words 
the  combining  weight  of  an  element,  determined  with  respect  to  a 


250  FUNDAMENTAL   PRINCIPLES   OF   CHEMISTRY 

second  element,  is  the  reciprocal  of  the  combining  weight  of  the 
second,  determined  with  respect  to  the  first.  The  proof  of  this 
depends  upon  the  fact  that  in  both  cases  we  are  dealing  with  the 
same  compound  AB  and  that  the  relation  by  weight  of  A  and  B, 
in  which  they  combine  to  form  this  substance,  or  in  which  they 
are  produced  during  its  decomposition,  is  definite  and  determined. 
If  a  is  the  weight  of  A  found  in  any  given  experiment,  and  b  is  the 

weight  of  B,  then  by  definition  (A)s  =  -  and  (B)A  =  -.   It  follows 

6  a 

immediately  that  (A)sX(B)A=I> 

This  relation  is,  however,  the  only  one  which  exists  between 
the  two  series,  for  no  other  compound  is  common  to  both.  If  we 
have  n  elements  each  of  them  has  n  —  1  combining  weights,  one 
for  each  of  the  other  elements.  The  number  of  these  combining 
weights  increases  without  limit  when  compounds  of  three  and  more 
elements  are  taken  account  of.  Beside  this,  compound  substances 
as  well  as  elements  have  combining  weights,  for  they  combine 
with  other  substances  to  form  more  complex  ones,  and  their  be- 
haviour can  be  described  by  the  law  of  integral  reactions.  This 
complexity  is  greatly  simplified  by  a  general  law  which  is  a  conse- 
quence of  the  law  of  the  conservation  of  the  elements  and  the  law 
of  integral  reactions. 

163.  TERNARY  COMPOUNDS  AND  THOSE  OF  HIGHER  ORDER.  - 
We  may  expand  the  law  of  constant  proportions  to  include  com- 
pounds of  three,  four,  or  any  number  of  elements.  Our  only  as- 
sumption was  that  we  should  deal  with  pure  substances,  and  not 
that  they  should  necessarily  be  elements.  If  therefore  the  com- 
pound AB  can  combine  with  the  element  C  to  form  a  compound 
ABC,  a  constant  relation  must  exist  between  the  weight  of  AB  and 
the  weight  of  C,  since  they  combine  to  form  the  pure  substance 
ABC. 

The  ternary  compound  ABC  can  also  be  formed  by  causing  the 
three  elements  to  react  with  one  another  simultaneously,  determin- 
ing the  proportion  in  which  a  pure  substance  and  not  a  solution  is 


THE   LAW  OF  COMBINING   WEIGHTS  251 

the  result  of  the  action.  We  can  in  this  way  determine  the  com- 
bining proportions,  and  in  this  case  these  are  for  the  elements  A,  B, 
and  C. 

The  composition  of  ABC  is  independent  of  the  way  in  which  it 
is  produced.  The  same  proportion  must  exist  whether  we  form 
ABC  from  AB  and  C,  or  from  A,  B,  and  C.  It  follows  therefore 
that  the  amount  of  AB  which  must  be  used  with  a  given  amount 
of  C  to  form  the  compound  ABC  is  the  sum  of  the  amounts  of  A 
and  B  which  we  must  use  with  the  same  amount  of  C.  In  other 
words,  the  combining  weight  of  AB  with  respect  to  C  is  the 
sum  of  the  combining  weights  of  A  and  B  with  respect  to  C,  both 
being  calculated  for  the  same  compound  ABC. 

Precisely  similar  considerations  hold  for  the  case  in  which  the 
compound  AC  is  first  prepared  and  then  combined  with  B  to  form 
ABC ;  or  we  could  first  make  BC  and  allow  this  to  combine  with 
A.  The  nature  of  a  substance  does  not  depend  upon  the  method 
of  its  preparation,  and  the  compounds  ABC,  ACB,  and  BCA  must 
be  regarded  as  identical.  The  weights  of  A,  B,  and  C  which  can 
be  made  from  these  compounds,  or  from  which  they  can  be  pre- 
pared, must  therefore  be  in  exactly  the  same  proportion  in  all  of 
them. 

The  following  important  conclusion  may  now  be  drawn  for  the 
substance  BC :  If  the  combining  proportion  of  B  with  respect  to 
A  and  that  of  C  with  respect  to  A  be  determined,  the  quantities 
which  combine  with  the  unit  weight  of  A  will  give  us  the  proportion 
by  weight  with  which  B  and  C  can  combine  with  each  other.  A 
in  this  case  has  nothing  whatever  to  do  with  the  matter,  for  B 
and  C  are  present  in  the  compound  ABC  in  the  proportion  in  which 
they  combine  singly  with  the  unit  of  A,  since  ABC  can  be  made 
from  AB  and  0,  and  from  AC  and  B.  ABC  can  also  be  made  by 
combining  BC  with  A,  and  B  and  C  are  therefore  present  in  ABC 
in  the  proportion  in  which  they  would  combine  to  form  BC.  This 
proportion  is  at  the  same  time  the  proportion  of  their  combining 
.weights  with  respect  to  A. 


252  FUNDAMENTAL   PRINCIPLES  OF  CHEMISTRY 

The  general  principle  may  now  be  stated :  If  the  combining  pro- 
portions of  the  elements  B,  C,  D,  etc.,  are  determined  with  respect 
to  an  element  A,  arbitrarily  chosen,  the  values  so  obtained  hold 
also  for  the  proportions  in  which  the  elements  B,  C,  D,  etc.,  will 
combine  with  each  other. 

With  the  aid  of  this  principle  it  is  evident  that  we  can  determine 
the  composition  of  compounds  which  we  have  never  analyzed 
quantitatively.  If  the  combining  proportions  A  :  B  and  A  :  C  have 
been  determined,  these  numbers  give  us  also  the  combining  pro- 
portions B :  (7,  although  the  substance  BC  has  not  been  analyzed 
or  even  prepared. 

This  result  raises  the  question  of  how  it  is  possible  to  know 
anything  about  a  thing  which  does  not  exist,  and  the  answer  is 
that  in  this  case  we  have  made  application  of  a  natural  law.  All 
natural  laws  possess  the  property  of  enabling  us  to  state  in  advance 
relations  which  are  still  unknown.  If  a  gas  is  produced  by  any 
operation  it  is  safe  to  state  beforehand  that  if  its  temperature  is 
raised  from  0°  to  100°  its  volume  will  increase  by  J^  of  its  volume 
at  0°,  assuming  that  the  pressure  is  kept  constant.  It  is  also  cer- 
tain that  if  it  is  kept  at  constant  volume  its  pressure  will  increase 
in  the  same  proportion.  All  those  substances  which  exhibit  the 
mechanical  properties  of  a  gas  have  so  far  in  our  experience  always 
exhibited  the  thermal  properties  of  a  gas,  and  I  am  therefore  able 
to  conclude  with  scientific  certainty,  that  is,  with  very  great  prob- 
ability, that  a  substance  about  which  I  know  nothing  more  than 
the  fact  that  it  behaves  mechanically  like  a  gas  will  also  behave 
thermally  as  such. 

The  natural  laws  of  which  we  have  made  use  in  the  foregoing 
reasoning  are  the  law  of  the  conservation  of  the  elements  and  the 
law  of  the  integral  reaction  of  compound  substances.  This  latter 
law  states  that  these  substances  can  combine  with  one  another 
without  the  separation  of  an  excess  of  any  one  of  their  elements. 
Both  of  these  laws  are  founded  on  experience,  as  all  natural  laws 
are,  and  they  are  limited  and  conditioned  by  experience.  For  the 


THE   LAW  OF  COMBINING  WEIGHTS  253 

present  we  must  consider  them  as  a  suitable  basis  for  further  con- 
clusions, for  the  conclusion  we  have  drawn  from  them  of  the  exist- 
ence of  combining  weights  has  been  strengthened  extensively  by 
experience.  Any  proof  of  chemical  proportions  which  may  be 
found  to  be  in  contradiction  with  the  law  of  the  combining  weights 
would  also  cast  doubt  on  these  more  general  laws,  and  we  would  be 
obliged  to  investigate  them  anew  in  the  light  of  this  new  experience. 

So  far  experience  has  been  in  complete  agreement  with  the  law 
of  the  combining  weights.  The  combining  weight  of  each  sub- 
stance which  has  been  regarded  as  an  element  has  been  determined 
with  respect  to  an  element  arbitrarily  chosen,  and  it  has  been  shown 
that  all  the  compounds  of  this  element  with  other  elements  can  be 
represented  by  the  proportion  of  the  corresponding  combining 
weights.  We  may  say,  in  short,  that  substances  combine  only  in 
the  proportion  of  their  combining  weights.  The  latter  are  specific 
properties  of  the  elements  alone,  independent  of  the  special  com- 
pound in  which  the  elements  are  present.  From  this  point  onward 
we  shall  indicate  by  A,  B,  C,  etc.,  not  only  the  elements  considered 
in  a  qualitative  way,  but  by  each  letter  we  shall  mean  one  combin- 
ing weight  of  the  element. 

164.  THE  COMBINING  WEIGHTS  OF  COMPOUND  SUBSTANCES.  - 
A  pure  substance  enters  and  leaves  a  chemical  compound  as  a  whole 
whether  it  is  an  element  or  a  compound.  It  therefore  has  its  own 
combining  weight,  and  the  value  of  this  weight  is  the  next  point  to 
discuss.  The  combining  weight  of  a  compound  substance  is  the 
sum  of  the  combining  weights  of  its  constituents.  Proof  of  this 
statement  is  contained  in  the  reasoning  of  Sec.  163.  The  com- 
pound ABC  can  be  produced  from  A,  B,  and  C,  or  from  AB  and  C. 
With  the  aid  of  the  law  of  the  conservation  of  the  elements,  and  by 
the  method  already  used,  it  can  be  shown  that  the  weight  of  AB 
which  combines  with  a  given  amount  of  C  is  the  sum  of  the  weights 
of  A  and  B  which  combine  with  the  same  amount  of  C.  The  above 
conclusion  follows  directly,  for  the  same  reasoning  is  applicable  to 
compound  substances  of  any  nature  whatever. 


254  FUNDAMENTAL   PRINCIPLES   OF   CHEMISTRY 

165.  THE  LAW  OF  RATIONAL  MULTIPLES.  —  In  the  preceding 
discussion  we  have  made  the  assumption  that  elements  combine 
in  only  one  proportion.  Our  conclusion  holds  therefore  only  for 
compounds  in  which  this  assumption  is  valid.  There  are,  how- 
ever, many  cases  in  which  two  elements  A  and  B  combine  in  more 
than  one  proportion,  and  we  shall  next  consider  the  laws  according 
to  which  these  combinations  take  place.  Let  us  first  of  all  ex- 
amine the  case  of  a  ternary  compound,  and  we  shall  suppose  that 
it  has  been  produced  by  the  union  of  a  substance  AB  with  an- 
other substance  AC.  The  resulting  substance  will  not  be  ABC, 
for  this  was  obtained  by  the  combination  of  AB  and  C.  The  new 
substance  contains  a  larger  amount  of  A  than  the  former  one. 
The  law  of  the  combining  weights  is  applicable  in  this  case,  for 
the  combining  weight  of  AB  is  the  sum  of  the  combining  weights 
of  A  and  B,  and  similarly  in  the  case  of  AC.  The  new  compound, 
which  we  shall  designate  with  ABAC,  because  of  the  way  in  which 
we  formed  it,  contains  the  element  A  twice  and  therefore  double 
the  combining  weight  of  A.  Twice  as  much  A  combines  with 
the  single  combining  weight  of  B  or  C  as  was  the  case  in  the 
compound  ABC. 

If  we  decompose  the  compound  ABAC  in  such  a  way  that  all 
of  C  separates  from  it,  a  substance  ABA  remains  which  contains 
the  double  combining  weight  of  A  in  combination  with  a  single 
combining  weight  of  B ;  and,  vice  versa,  if  a  substance  exists  which 
combines  with  C  to  form  the  new  compound  ABAC,  this  substance 
must  contain  two  combining  weights  of  A  to  one  of  B. 

This  method  of  reasoning  can  be  carried  as  far  as  we  choose. 
It  is  independent  of  the  nature  of  the  elements  and  compounds 
involved,  and  the  only  assumption  required  is  the  validity  of  the 
two  general  laws  of  the  conservation  of  the  elements  and  the  in- 
tegral reaction  of  compound  substances.  The  result  can  be  stated 
in  its  most  general  form  in  the  following  way:  If  elements  com- 
bine in  several  proportions  by  weight,  combination  takes  place  be- 
tween the  corresponding  multiples  of  their  combining  weights. 


THE   LAW   OF  COMBINING  WEIGHTS  255 

Operations  of  combination  and  separation,  similar  to  those 
applied  to  AB,  can  also  be  carried  out  upon  the  compound  ABC, 
and  in  this  way  we  can  proceed  step  by  step  to  compounds  con- 
taining three,  four,  five,  etc.,  combining  weights  of  A.  Any  other 
element  can  take  the  place  of  A,  and  this  justifies  the  generaliza- 
tion we  have  just  made.  It  is  also  evident  from  the  derivation 
of  this  principle  that  the  law  holds  for  binary,  ternary,  and  higher 
compounds.  We  can  replace  the  elements  A,  B,  and  C  by  any 
compounds  whatever,  provided  they  fit  our  assumption  that  pure 
substances  are  to  be  used,  and  in  this  way  the  proof  may  be  ex- 
tended to  compounds  as  complex  in  nature  as  we  wish.  »  . 

It  follows  from  this  that  the  composition  of  any  pure  substance 
can  be  expressed  by  a  formula  of  the  form,  mA,  nB,  pC,  qD,  etc., 
ra,  ??,  p,  and  q  being  whole  numbers.  Experience  has  shown  that 
m,  n,  etc.,  are  usually  small  numbers,  although  values  of  100  or 
more  have  been  observed.  The  proof  of  the  law  becomes  more 
difficult,  however,  as  these  numbers  become  greater,  for  the  differ- 
ence in  the  quantitative  composition,  corresponding  to  the  dif- 
ference of  one  unit  of  the  combining  weight,  becomes  smaller  and 
smaller.  If,  for  example,  m  is  100,  a  substance  of  analogous  com- 
position in  which  m  is  101  would  show  on  analysis  a  difference  of 
only  1  per  cent  in  its  content  of  the  element  A. 

166.  CHEMICAL  FORMULAE. — The  law  of  combining  weights 
states  that  all  substances  enter  into  chemical  reaction  only  in 
definite  proportions  by  weight,  and  that  these  proportions  are 
independent  of  the  nature  of  the  elements  which  take  part  in  the 
reaction.  It  gives  us  a  very  simple  and  evident  means  of  describ- 
ing the  relations  between  elements  and  their  compounds,  and  we 
have  already  made  use  of  it.  For  scientific  purposes  it  is  neces- 
sary to  represent  these  definite  relations  between  elements  and 
their  compounds  by  definite  symbols.  Each  compound  is  desig- 
nated by  a  combination  of  the  symbols  of  the  elements  from 
which  it  can  be  produced  and  into  which  it  can  be  decomposed. 
If  A,  B,  C,  etc.,  are  symbols  for  the  elements,  AB  is  a  symbol  of 


256  FUNDAMENTAL  PRINCIPLES  OF  CHEMISTRY 

a  compound  which  can  be  produced  from  elements  A  and  $,  and 
ABC  is  the  symbol  of  a  compound  from  which  the  elements  A, 
B,  and  C  can  be  obtained.  The  designation  is  so  far  only  a  qualita- 
tive one;  it  states  the  elements  which  exhibit  the  above-mentioned 
definite  synthetic  and  analytic  relation  to  a  given  compound. 
With  the  aid  of  the  law  of  the  combining  weights  these  symbols 
can,  however,  become  quantitative.  It  is  only  necessary  to  give 
to  the  symbol  for  an  element  a  further  meaning.  It  must  represent 
one  combining  weight  of  the  corresponding  element.  Elements 
combine  only  in  the  proportion  of  their  combining  weights,  or 
their  multiples,  and  we  have  indicated  no  limitation  by  thus  ex- 
panding the  meaning  of  the  symbol.  Substances  not  included  in 
this  class  are  not  compounds  but  only  solutions,  and  this  is  there- 
fore a  further  means  of  discriminating  between  pure  substances 
and  solutions. 

It  must  also  be  kept  in  mind  that  elements  combine  not  only 
in  the  simple  proportion  of  their  combining  weights,  but  also  in 
multiples  of  them.  A  number  is  added  to  the  symbol  for  each 
element,  and  this  number  indicates  how  many  combining  weights 
of  the  element  take  part  in  the  formation  or  decomposition  of  the 
compound  in  question.  A  formula  AmBnCp  designates  a  sub- 
stance which  is  made  up  of  m  combining  weights  of  A,  n  combin- 
ing weights  of  B,  and  p  combining  weights  of  C.  It  is  evident  that 
this  formula  also  expresses  the  fact  that  the  combining  weights 
of  compound  substances  are  the  sum  of  the  combining  weights  of 
their  constituents. 

A  formula  of  this  kind  suggests  an  idea  which  needs  careful 
consideration  and  one  which  is  very  often  misunderstood.  The 
symbols  for  the  elements  make  up  the  symbols  of  compounds, 
and  this  suggests  the  thought  that  the  elements  are  actually  physi- 
cally present  in  their  compounds  just  as  their  symbols  are  present 
in  the  symbol  of  the  compound.  It  is  however  characteristic  of 
a  chemical  process  that  substances  should  disappear,  and  that 
others  with  other  properties  should  take  their  place.  The  ele- 


THE   LAW  OF  COMBINING  WEIGHTS  257 

ments  and  their  properties  disappeared  when  the  compound  was 
formed,  and  it  is  therefore  impossible  that  an  element  should  per- 
sist in  its  compounds.  The  idea  that  the  elements  have  disappeared, 
but  are  nevertheless  present  as  such,  is  an  indefinite  one,  too  in- 
definite for  scientific  use.  The  elements  can  be  recovered  from 
their  compounds  whenever  we  choose,  and  this  is,  as  a  matter  of 
fact,  all  that  we  can  say  about  them.  It  is  somewhat  analogous 
to  what  happens  when  an  amount  of  money  of  various  denomina- 
tions is  taken  to  the  bank  for  safe  keeping.  The  same  amount 
can  be  obtained  from  the  bank  in  the  same  denominations  at  any 
time.  It  by  no  means  follows  that  the  bank  has  kept  the  coins 
paid  in  during  the  whole  time,  but  only  that  the  bank  has  means 
sufficient  to  return  our  deposit.  What  becomes  of  the  coins  in 
the  meantime  we  do  not  know,  nor  is  it  a  matter  of  importance. 
A  compound  can  at  any  time  be  transformed  into  its  elements 
again,  but  we  can  only  conclude  from  this  that  the  condition  for 
the  formation  of  the  elements  always  exists,  and  not  that  the  ele- 
ments persist  as  individuals  in  the  compound.  Certain  proper- 
ties of  the  elements,  their  weight,  for  example,  are  conserved  in 
the  compound,  but  a  given  weight  cannot  be  changed  by  any 
process  whatever,  and  this  fact  affords  no  proof  for  the  persistence 
of  the  elements  in  a  compound. 

The  question  is  not,  Are  the  elements  contained  '*  as  such  " 
in  the  compound  ?  The  answer  to  this  question  is  decidedly  a 
negative  one,  for  the  properties  of  the  elements  are  not  retained 
in  the  compound  as  the  properties  of  the  individual  gases  in  a 
gaseous  solution  are.  A  much  more  important  question  is  the 
following:  Are  there  other  properties  of  the  elements  beside 
weight  (and  mass)  which  are  retained  in  compounds?  Can  any 
connection  be  traced  between  the  properties  of  elements  and  those 
of  their  compounds?  The  answer  is  a  complicated  one,  and  it 
forms  the  content  of  an  extended  chapter  of  scientific  chemistry. 
Here  we  can  only  say  that  no  property  of  the  elements,  except 
mass  and  weight,  is  conserved  unchanged  in  a  compound,  but 
17 


258  FUNDAMENTAL  PRINCIPLES  OF  CHEMISTRY 

approximate  agreement  in  properties  is  quite  common.  The 
properties  of  the  compound  can  sometimes  be  represented  as  the 
sum  of  the  properties  of  their  elements.  These  relations  are,  how- 
ever, not  exact  ones,  and  the  degree  of  their  exactness  varies  with 
the  nature  of  the  properties  in  question.  Many  properties  of  com- 
pounds show  no  apparent  relation  whatever  to  those  of  the  elements 
from  which  they  are  made. 

167.  CHEMICAL  EQUATIONS.  —  Chemical  formulae  serve  to  de- 
scribe chemical  processes  as  well  as  in  the  representation  of  the 
composition  of  a  compound. 

This  application  is  based  on  the  law  of  the  conservation  of  the 
elements,  which  states  that  if  we  start  with  given  substances  con- 
taining certain  elements  we  can  only  make  those  substances  which 
contain  these  same  elements.  Further,  the  compounds  produced 
contain  the  elements  only  in  such  proportion  that  the  total  amount 
of  each  element  remains  unchanged  after  the  transformation.  It 
is  customary  to  speak  of  the  presence  of  the  elements,  because  of 
the  fact  that  the  elements  in  question  can  always  be  produced 
from  the  compound  in  their  original  amounts. 

Since  elements  are  characterized  in  this  way  in  the  chemical 
formulae  for  compounds,  the  following  condition  must  be  ful- 
filled if  any  chemical  process  is  to  be  represented  by  a  formula. 
The  same  elements  must  be  present  in  the  same  amounts,  that 
is,  an  equal  number  of  combining  weights  of  each  element  must  be 
indicated  before  and  after  the  reaction. 

It  is  therefore  customary  to  write  chemical  reactions  in  the 
form  of  equations,  the  original  substances  being  placed  at  the 
left  and  the  resulting  substances  at  the  right,  the  two  sets  of  sub- 
stances being  connected  by  the  sign  = .  If  an  equation  is  correct 
the  same  number  of  combining  weights  of  each  element  must  be 
found  on  the  two  sides  of  the  equation,  otherwise  the  law  of  the 
conservation  of  the  elements  would  not  hold. 

This  is,  however,  only  a  necessary  and  not  a  sufficient  condi- 
tion for  the  possibility  of  a  chemical  process.  There  would  be  no 


THE   LAW  OF  COMBINING   WEIGHTS  259 

difficulty  in  arranging  a  given  finite  number  of  combining  weights 
of  various  elements  in  very  many  different  ways,  and  so  setting 
up  between  two  such  groups  equations  which  would  be  correct 
as  far  as  the  law  of  conservation  is  concerned.  Such  an  equa- 
tion would,  however,  by  no  means  always  express  an  actual  possible 
process.  Many  groups  of  elements  are  unknown  as  compound 
substances,  and  not  every  transformation  which  obeys  the  law  of 
the  conservation  of  the  elements  is  experimentally  possible.  Like 
all  other  natural  laws  the  law  of  conservation  enables  us  to  draw 
a  line  within  which  all  actual  reactions  take  place,  though  by  no 
means  all  the  cases  which  lie  within  this  line  are  practically  possi- 
ble. In  fact  only  a  comparatively  small  number  of  them  may 
have  experimental  existence.  Which  of  them  have  real  existence, 
and  how  we  can  discriminate  between  the  actual  cases  and  those 
which  are  merely  formally  possible,  can  only  be  determined  with  the 
aid  of  other  special  laws  which  cannot  be  taken  up  at  this  point. 
The  chemical  reactions  which  can  be  represented  by  such  an 
equation  are  of  two  kinds.  It  very  frequently  happens  that  a 
chemical  process  takes  place  only  in  one  direction  and  not  in  the 
opposite  direction.  If,  for  example,  two  mutually  soluble  liquids 
are  brought  into  contact  they  form  a  solution,  but  this  solution 
does  not  separate  of  its  own  accord  into  its  constituents.  If,  how- 
ever, we  have  a  mixture  of  ice  and  water,  the  amount  of  water  can 
be  increased  at  the  expense  of  the  ice  by  the  addition  of  heat,  and 
the  opposite  process  can  be  brought  about  by  taking  away  heat. 
Chemical  processes  in  the  narrower  sense  show  the  same  differences. 
Many  of  them  take  place  in  a  definite  direction  and  reasonable 
changes  in  the  external  conditions  produce  no  noticeable  effect 
upon  them.  There  are,  however,  other  processes  which  can  be 
reversed  by  changes  in  the  external  conditions.  The  first  of  these 
is  called  a  unidirectional  or  complete  reaction,  the  other  involves 
a  chemical  equilibrium.  It  is  often  desirable  in  writing  a  chemical 
equation  to  make  it  clear  which  of  these  two  processes  is  described 
by  the  equation. 


260  FUNDAMENTAL  PRINCIPLES  OF  CHEMISTRY 

When  this  is  desirable  the  equality  sign  is  replaced  by  a  symbol 
which  indicates  the  direction  of  the  process,  and  this  is  usually 
an  arrow  or  a  similar  symbol.  The  symbol  =£  is  used  to  de- 
scribe a  unidirectional  or  complete  process,  the  arrow-points  in- 
dicating the  direction  in  which  it  takes  place.  When  we  wish  to 
describe  a  chemical  equilibrium  we  make  use  of  the  symbol  ±=^, 
which  expresses  the  possibility  of  a  reaction  in  either  direction. 
If  there  is  no  particular  reason  for  characterizing  one  or  the  other 
of  these  cases,  the  ordinary  equality  sign  should  be  used. 

168.  METHODS  OF  DETERMINING  COMBINING  WEIGHTS.  —  The 
most  direct  method  of  determining  the  combining  weight  of  an 
element  is  to  cause  it  to  combine  with  the  standard  element,  de- 
termining the  combining  proportion  by  analysis  or  synthesis.  For 
this  reason  the  element  which  forms  the  largest  number  of  com- 
pounds with  the  other  elements  should  be  chosen  as  standard.  In 
many  cases  this  simple  process  is  not  applicable,  for  the  analysis 
of  compounds  so  produced  is  sometimes  one  of  special  difficulty, 
and  therefore  less  accurate  than  the  analysis  of  other  compounds 
of  the  same  element.  The  following  general  rule  is  applicable: 
If  we  determine  the  proportion  in  which  the  element  to  be  in- 
vestigated, X,  combines  with  one  combining  weight  of  any  other 
element,  B,  we  have  determined  the  combining  weight  of  X,  that 
is,  the  amount  of  X  which  will  combine  with  one  combining  weight 
of  the  standard  element  A.  This  rule  follows  directly  from  the 
general  law  that  the  elements  combine  only  in  the  proportions  of 
their  combining  weights.  The  amounts  of  X  and  of  B  which  com- 
bine with  the  combining  weight  of  the  standard  element  A  are  in 
the  same  proportion  as  the  amounts  in  which  they  combine  with 
each  other,  and  this  proves  the  correctness  of  the  method  just 
applied. 

There  are  cases  in  which  the  process  just  described  cannot  be 
conveniently  applied.  In  place  of  a  compound  of  X  with  one 
other  element  it  is  sometimes  necessary  to  choose  a  compound 
of  X  with  several  other  elements.  The  most  general  method  of 


THE   LAW  OF   COMBINING  WEIGHTS  261 

solving  the  problem  consists  not  in  the  use  of  the  element  X  as 
such,  but  in  using  compounds  of  this  element.  For  example,  the 
problem  may  be  solved  by  transforming  a  substance  XBC  into 
another  substance  XDEF. 

In  all  of  these  cases  the  combining  weights  of  all  the  elements 
involved  must  be  known,  with  the  exception  of  that  of  X.  We 
obtain  in  this  way  an  equation  representing  the  chemical  trans- 
formation and  containing  the  weights  of  all  the  elements  except  X. 
Solution  of  this  equation  gives  the  desired  value  for  X. 

It  must  be  kept  in  mind  that  all  of  these  combining  weights 
which  we  assume  to  be  known  have  been  determined  experimen- 
tally. Each  of  them  has  therefore  its  probable  error,  and  the  value 
of  this  error  depends  upon  the  nature  of  the  individual  element. 
The  result  obtained  from  the  numerical  equation  involving  these 
numbers  involves  also  all  of  these  errors,  which  increase  the  prob- 
able error  of  the  combining  weight  to  be  determined.  For  the  sake 
of  exactness  it  is  best  to  involve  as  few  combining  weights  as  pos- 
sible, and  from  this  point  of  view  the  simplest  methods  for  deter- 
mining the  combining  weights  are  the  best. 

The  combining  weights  are  the  real  units  of  chemical  arithmetic. 
If  the  combining  weight  of  B  is  large,  a  large  amount  of  B  combines 
with  a  given  amount  of  A.  If  C  has  a  small  combining  weight,  a 
small  amount  of  C  combines  with  the  same  amount  of  A.  If  our 
calculations  are  to  be  accurate,  the  various  combining  weights 
should  be  known  with  the  same  percentage  accuracy. 

On  the  other  hand,  we  add  combining  weights  when  we  calculate 
the  combining  weight  of  a  compound.  The  laws  of  probability 
show  that  the  absolute  probable  error  and  not  the  relative  one 
should  be  equal  for  each  element  if  the  accuracy  of  our  result  for 
a  compound  is  to  be  least  affected. 

Finally,  it  should  be  noticed  that  the  accuracy  of  the  combining 
weights  at  the  present  time  is  dependent  in  a  large  degree  upon  the 
rarity  of  occurrence  of  an  element  and  upon  its  common  applica- 
tion. The  combining  weights  of  the  most  important  elements  have 


262  FUNDAMENTAL  PRINCIPLES   OF  CHEMISTRY 

been  the  subject  of  much  more  investigation  than  those  of  the  rare 
ones,  and  they  are  therefore  much  more  accurate. 

As  science  has  advanced  the  accuracy  of  our  knowledge  of  the 
combining  weights  has  constantly  increased,  and  their  numerical 
values  show  a  corresponding  change.  We  now  have  international 
usage  in  atomic  weights  just  as  we  have  units  of  length  and  weight. 
The  international  committee  publishes  a  table  every  year  giving 
the  most  probable  values  for  the  combining  weights,  and  these  are 
used  by  all  chemists  in  their  calculations.  This  will  make  it  easy 
in  the  future  to  determine  what  combining  weights  are  used  in 
any  research,  even  though  the  author  has  not  mentioned  them  in 
his  paper.  This  condition  of  things  dates  only  from  the  year  1902, 
and  in  all  earlier  researches  great  uncertainty  in  this  matter  is  the 
rule,  unless  the  combining  weights  which  were  used  are  mentioned 
by  the  author. 

169.  THE  INDEFINITENESS  OF  THE  COMBINING  WEIGHTS.  - 
The  choice  of  combining  weights  is  an  arbitrary  one  for  two  reasons, 
even  though  no  doubt  remains  concerning  the  relations  by  weight 
which  are  to  be  used  in  calculating  chemical  results.  First,  the 
choice  of  the  standard  element  is  an  arbitrary  one;  and,  second, 
when  the  same  elements  form  several  compounds  we  must  choose 
arbitrarily  which  compound  we  will  assume  to  contain  equal  com- 
bining weights  of  the  elements  in  question. 

We  have  already  considered  one  point  in  connection  with  the 
first  question.  Tables  of  combining  weights  based  on  different 
standard  elements  are  always  proportional,  for  it  is  always  pos- 
sible to  deduce  the  same  combining  proportion  for  any  compound 
from  any  table.  It  is  therefore  a  matter  of  secondary  importance 
which  element  is  chosen  as  the  standard.  At  present  chemists  are 
united  in  using  oxygen  as  the  standard.  This  element  occurs  most 
profusely  on  the  earth's  surface.  About  one  half  of  all  the  sub- 
stances which  make  up  the  earth's  crust  is  oxygen. 

We  must  look  for  an  answer  to  the  second  point  in  the  law  of 
rational  multiples,  as  applied  to  compounds  which  contain  the 


THE   LAW  OF  COMBINING   WEIGHTS  263 

same  elements  in  several  proportions.  If  we  have,  for  example, 
two  compounds  of  A  and  B,  the  second  of  which  contains  twice  as 
much  B  as  the  first,  their  formulae  may  be  written  either  AB  and 
AB2,  or  A2B  and  AB.  We  assume  in  the  first  case  that  the  first 
of  the  two  compounds  contains  equal  combining  weights.  In  the 
second  case  we  must  assume  that  two  combining  weights  of  B 
enter  the  compound.  In  the  other  case  we  assume  that  the  second 
compound  is  the  normal  one  with  the  formula  AB,  and  then  the 
first  compound  must  be  assumed  to  contain  two  combining  weights 
of  At  since  it  contains  the  same  amount  of  B  combined  with  twice 
as  much  A  as  in  the  second  compound.  In  the  second  case  the 
combining  weight  of  A  must  be  twice  as  great  as  in  the  first  case, 
or  the  combining  weight  of  B  must  be  half  as  great.  Taken  by 
itself  the  law  of  the  combining  weights  affords  no  means  of  dis- 
criminating between  these  possibilities,  nor  is  the  law  of  rational 
proportions  of  any  assistance.  Both  laws  hold  true  whichever 
assumption  is  made.  The  freedom  of  choice  which  is  left  us  in 
this  case  can  be  used  for  the  purpose  of  expressing  other  relations, 
and,  as  a  matter  of  fact,  the  volume  relations  of  gases  afford  a 
means  of  making  a  definite  choice  between  the  various  possibilities. 
Other  facts  lead  us  to  a  simple  and  useful  set  of  relations,  but  the 
final  reasons  for  the  choice  of  combining  weights  cannot  be  taken 
up  here.  It  need  only  be  said  that  we  have  finally  arrived  at  a 
definite  decision  which  has  been  accepted  by  all  chemists. 

170.  THE  GENERAL  RELATIONS  OF  THE  COMBINING  WEIGHTS. 
—  Combining  weights  are  of  use  not  only  in  describing  in  the 
broadest  way  the  relations  by  weight  which  exist  between  com- 
pounds and  their  elements,  but  they  also  have  other  important 
functions.  Other  properties  of  substances  show  simple  sets  of  rela- 
tions when  they  are  calculated  on  the  basis  of  combining  weights, 
provided  these  properties  can  be  stated  as  functions  of  the  amount 
of  substances  involved.  The  most  evident  way  of  expressing  such 
properties  is  to  refer  them  to  the  unit  of  weight.  This  method  of 
reference  is  in  fact  a  general  one  in  physics,  and  the  definition  of 


264  FUNDAMENTAL  PRINCIPLES  OF  CHEMISTRY 

specific  volume  given  in  Sec.  12  is  one  of  many  examples  of  its 
use.  As  far  as  chemistry  is  concerned,  it  is  usually  best  to  refer  the 
volume  occupied  by  a  given  substance  not  to  the  gramme,  but  to  the 
number  of  grammes  of  the  substance  which  is  equal  to  the  combin- 
ing weight.  Especially  in  the  case  of  gases  volumes  so  calculated 
are  either  equal  or  in  some  rational  proportion.  Among  liquids 
and  solids  we  have  no  such  simple  relation,  but  in  many  cases 
their  volumes  can  be  represented  as  sums  made  up  of  the  volumes 
which  can  be  given  to  the  combining  weights  of  the  elements. 
Similar  simple  relations  have  also  been  found  for  many  other  prop- 
erties, and  it  is  now-a-days  customary  in  chemistry  to  express  all 
the  properties  which  permit  such  usage  in  terms  of  the  combining 
weights. 

Considered  as  quantities,  the  combining  weights  are  the  units 
for  the  capacity  factor  of  chemical  energy.  The  capacity  factor 
itself  is  expressed  by  the  number  of  these  units  which  enter  a  given 
system,  in  other  words,  the  weights  of  substances  taking  part  must 
be  divided  by  their  combining  weights  to  find  the  number  of  these 
units  involved.  It  is  evident  that  in  calculations  of  this  kind  the 
amounts  of  various  substances  which  combine  with  each  other, 
or  react  chemically  with  each  other,  will  be  expressed  by  equal 
numbers,  or,  in  case  multiple  proportions  are  involved,  by  numbers 
which  are  in  simple  rational  proportions  to  each  other. 

A  system  of  this  kind  is  in  general  use  in  analytical  chemistry. 
Solutions  of  various  substances  are  prepared  which  contain  a  com- 
bining weight  in  grammes  or  a  simple  fraction  of  this  amount,  in  a 
litre  of  solution.  Such  solutions  react  with  each  other  in  simple 
proportions  by  volume,  and  when  a  certain  volume  of  such  a  solu- 
tion has  been  used  in  a  given  reaction  with  another  body,  measure- 
ment of  the  volume  is  sufficient  to  enable  us  to  calculate  the  amount 
of  the  corresponding  substance  in  the  body  under  investigation. 
This  method  of  determining  the  amount  of  a  substance  is  called 
volumetric  analysis. 


<^v£**^ 

*V*  OF   THE 

UNIVERSITY 


CHAPTER  VIII 
COLLIGATIVE   PROPERTIES 

171.  THE  LAW  OF  GAS  VOLUMES.  —  In  our  consideration  of 
the  general  law  of  constant  combining  proportions  it  was  men- 
tioned that  among  gases  we  would  find  another  law  of  constant 
volume  proportions.     All  gases  change  their  volume  in  the  same 
proportion  under  the  influence  of  changes  in  pressure  and  tem- 
perature, and  when  two  gas  volumes  have  been  measured  under 
definite  conditions  their  ratio  remains  the  same  whatever  changes 
may  be  made  in  their  common  pressure  and  temperature.    If  we 
examine  the  numerical  values  of  the  volumes  in  which  gases  react 
with  one  another  we  find  the  following  experimental  law:   The 
volumes  are  either  equal  or  in  simple  rational  proportion. 

This  law  holds  not  only  for  the  case  of  two  gases  which  are 
combining  or  reacting,  but  also  for  all  cases  where  gases  appear  or 
disappear.  If  gaseous  substances  appear  as  two  or  more  members 
of  a  reaction  equation,  the  gases  always  exhibit  simple  proportions 
by  volume,  provided  they  are  measured  at  the  same  pressure  and 
temperature. 

The  most  general  method  of  representing  the  amount  of  gas, 
independent  of  temperature  and  pressure,  is  given  by  the  value  of 

PV 

r  in  the  gas  equation  PV=rT,  for  in  this  equation  we  have  r  =  —=-. 

In  this  form  the  gas  law  may  be  expressed  as  follows:  If  two  or 
more  gases  take  part  in  a  chemical  reaction  their  r  values  are 
either  the  same  or  in  a  simple  rational  proportion. 

172.  THE  RELATION  TO  THE  COMBINING  WEIGHTS.  —  If  the 
law  just  expressed  is  compared  with  the  law  of  the  combining 

265 


266  FUNDAMENTAL   PRINCIPLES  OF  CHEMISTRY 

weights  a  remarkable  conclusion  may  be  drawn.  It  is  as  follows : 
Amounts  of  different  gases  which  correspond  to  the  same  r  values 
must  be  either  in  the  proportion  of  the  combining  weights  or  in  the 
proportion  of  simple  rational  multiples  of  them. 

This  law  follows  from  the  two  following  laws : 

All  gases  combine  in  the  proportion  of  their  combining  weights. 

All  gases  combine  in  equal  volumes  or  in  volumes  which  are  in 
rational  proportion  to  each  other. 

It  follows  directly  that  equal  gas  volumes  are  those  which  are 
in  simple  rational  proportion,  corresponding  to  weights  which  are 
proportional  to  the  combining  weights. 

Furthermore,  the  weights  of  equal  volumes  of  gases  are  numeri- 
cally the  same  as  the  densities  of  the  gases  if  they  are  based  upon 
the  unit  of  volume.  It  follows  therefore  that: 

The  densities  of  various  gases  are  in  the  same  proportion  as  the 
combining  weights  of  the  gases,  or  simple  multiples  of  them. 

Because  of  this  direct  relation  it  is  possible  to  deduce  the  law  of 
the  combining  weights  from  that  of  rational  volume  proportions. 
Suppose  we  have  the  same  volume  of  any  number  of  gases,  a  litre, 
for  example  (or,  in  general,  amounts  of  the  gases  which  have  the 
same  r),  it  will  then  be  possible  to  carry  out  all  the  combinations, 
decompositions,  or  other  chemical  processes  in  which  these  gases 
take  part  in  such  a  way  that  the  total  volume  of  each  gas  will  always 
take  part  in  the  reaction.  All  chemical  processes  will  take  place 
between  whole  litres,  though  it  will  be  necessary  of  course  to  use  in 
some  cases  two,  three,  or  some  other  number  of  whole  litres  in  the 
reaction,  but  in  no  case  will  a  fraction  of  a  litre  be  used  or  produced. 
If  we  call  the  weight  of  a  litre  of  each  of  these  gases  its  combining 
weight,  then  it  is  evident  that  gases  combine  with  each  other  only 
in  the  proportions  of  their  combining  weights,  or  integral  multiples 
of  them. 

So  far  we  know  this  only  for  gases,  but  a  high  enough  tempera- 
ture and  low  enough  pressure  are  theoretically  the  only  conditions 
which  must  be  fulfilled  to  transform  any  substance  into  a  gas. 


COLLIGATIVE   PROPERTIES  267 

There  is  therefore  no  fundamental  reason  to  place  a  limit  on  the 
application  of  this  law,  and  it  can  be  extended  to  include  all  sub- 
stances with  scientific  probability.  It  is,  to  be  sure,  impossible  to 
prove  the  gas  law  experimentally  for  all  substances,  since  in  many 
cases  our  means  are  insufficient  to  change  substances  into  gases 
and  investigate  them  in  this  condition.  It  is,  however,  possible 
to  investigate  the  law  of  the  combining  weights,  which  has  been 
derived  from  this  law,  for  all  substances,  and  it  has  been  shown 
in  the  previous  chapter  that  the  law  of  the  combining  weights 
describes  the  facts  accurately. 

The  inverse  process,  i.  e.  the  derivation  of  the  law  of  gas  volumes 
from  the  law  of  the  combining  weights,  cannot  be  carried  out. 
This  means  that  the  former  law  is  the  more  general  one,  and  that 
the  gas  volume  law  contains  in  itself,  not  only  the  law  of  the 
combining  weights,  but  also  another  law  relating  to  the  gaseous 
state. 

173.  COMBINING  WEIGHT  AND  MOLAR  WEIGHT.  —  The  direct 
relation  between  combining  weight  and  gas  density  suggests  the  idea 
that  we  might  make  use  of  the  freedom  left  us  in  the  choice  of  the 
rational  factor  of  the  combining  weights  (see  Sec.  169),  and  that 
we  might  make  these  two  things,  combining  weight  and  gas  density, 
proportional,  or  even  equal,  by  a  proper  choice  of  units.  This 
idea  was  suggested  soon  after  the  discovery  of  the  density  relations 
between  gases,  but  it  leads  to  consequences  which  force  us  to 
reject  it.  It  is  impossible  for  us  to  have  combining  weight  and  gas 
density  equal,  and  at  the  same  time  to  satisfy  the  requirement  that 
the  combining  weight  of  compounds  should  be  equal  to  the  sum 
of  the  combining  weights  of  the  elements  involved. 

In  order  that  these  two  principles  should  hold  at  the  same  time, 
the  volume  of  the  compound  in  the  gaseous  state  must  never  be 
larger  than  the  smallest  volume  of  the  gaseous  elements  which  take 
part.  Suppose  we  have  a  chemical  reaction  between  gases  repre- 
sented by  the  equation  mA  +nB+pC,  etc.=rD+sE,  etc.,  m,  n,  p, 
etc.,  and  r,  s,  etc.,  representing  the  number  of  volumes  of  each 


268  FUNDAMENTAL  PRINCIPLES   OF  CHEMISTRY 

gas,  arranged  in  order  of  magnitude  (m  >  n  >  p,  etc.),  r  can  never 
be  greater  than  m,  for  it  must  be  equal  to  m  or  a  rational  fraction 
of  m.  Experiment  has,  however,  shown  numerous  cases  where  r 
is  greater  than  m,  and  if  this  is  the  case  unit  volume  of  D  contains 
a  fraction  of  the  combining  weight  of  A,  and  the  composition  of  D 
cannot  be  represented  in  round  numbers  as  the  sum  of  the  combin- 
ing weights  of  its  elements. 

Experiment  shows  that  it  is  impossible  to  choose  combining 
weights  in  the  ratio  of  the  gas  densities,  and  at  the  same  time  apply 
the  principle  that  the  combining  weights  of  compounds  shall  be 
the  sum  of  the  combining  weights  of  their  elements.  One  of  these 
two  principles  must  be  given  up,  and,  so  far  as  our  discussion  has 
shown,  it  makes  no  difference  which  of  the  two  this  is.  There  are, 
however,  cases  where  the  gas  density  of  an  element,  i.  e.  the  con- 
stant r,  has  been  shown  to  be  variable  with  pressure  and  tempera- 
ture, and  therefore  our  original  choice,  by  which  we  gave  up 
proportionality  between  gas  density  and  combining  weight,  is 
justified.  We  have  retained  the  other  principle  by  which  combin- 
ing weights  of  compounds  are  made  up  as  the  sum  of  the  combining 
weights  of  their  elements,  premising  in  this  that  no  fraction  of  com- 
bining weights  shall  appear  in  our  formula?. 

In  order  to  express  the  law  of  gas  volumes  conveniently  and 
simply,  we  have  introduced  a  new  concept  to  represent  the  weight 
of  equal  gas  volumes,  indicating  their  close  relation  to  combin- 
ing weights.  The  weights  of  equal  gas  volumes  are  called  molar 
weights. 

Molar  weights  are  chosen  as  nearly  like  combining  weights  as 
possible.  It  follows  from  the  relations  just  discussed  that  the 
molar  weights  of  those  elements  which  form  gaseous  compounds 
of  greater  volume  must  be  chosen  greater  than  the  combining 
weights  in  the  same  proportion,  i.  e.  the  molar  weight  of  the  ele- 
ment will  be  to  the  combining  weight  of  the  element  as  the  com- 
bining volume  is  to  the  volume  of  the  element.  Experiment  has 
shown  that  this  proportion  is  equal  to  two  for  many  elements. 


COLLIGATIVE   PROPERTIES  260 

These  elements  never  form  gaseous  compounds  whose  volume  is 
greater  than  twice  that  of  their  own  volume.  It  is  therefore 
sufficient  to  make  the  molar  weight  of  such  elements  twice  the 
combining  weight  in  order  to  avoid  fractions  in  the  writing  of 
formulae. 

This  settles  the  question  concerning  freedom  of  choice  of  the 
rational  factor  for  the  combining  weights.  The  molar  weight  is  by 
definition  proportional  to  the  gaseous  density  under  normal  condi- 
tions of  pressure  and  temperature.  The  proportionality  factor  has 
been  so  chosen  that  the  molar  weight  of  a  compound  is  the  same 
as  its  combining  weight,  while  for  the  elements  mentioned  above 
the  molar  weight  is  twice  the  combining  weight. 

There  are  a  few  elements  in  which  this  relation  does  not  hold. 
Some  of  them  form  gaseous  compounds  whose  volume  is,  at  the 
most,  equal  to  the  volume  of  the  element,  or  in  some  cases  a  rational 
fraction  of  it.  The  molar  weight  of  such  elements  is  chosen  equal 
to  the  combining  weight.  There  are  also  elements  which  enter 
combination  in  four  times  the  elementary  volume.  Their  molar 
weight  is  therefore  four  times  their  combining  weight.  In  all 
these  cases,  however,  the  relation  once  chosen  holds  for  all  gaseous 
compounds  of  the  same  element.  An  element  which  enters  com- 
pounds with  four  times  its  elementary  volume  does  not  form  com- 
pounds in  which  a  triple  volume  or  one  five  times  the  elementary 
volume  is  active.  The  deviations  observed  are  cases  in  which,  a 
rational  fraction  of  the  larger  combining  volume  is  found.  For 
example,  these  same  elements  form  occasional  compounds  whose 
gas  volumes  are  only  twice  that  of  the  elementary  volume  instead 
of  four  times.  In  these  cases  we  must  assume  that  two  combin- 
ing weights  of  the  element  must  be  used  in  writing  the  molar 
formula  for  the  compound.  If  m  represents  the  greatest  multiple 
of  the  elementary  volume  in  which  an  element  enters  into  com- 
bination, any  other  volume  relation  of  this  element  can  be  repre- 
sented by  the  fraction  — ,  n  being  a  whole  number,  showing  the 
n 


270  FUNDAMENTAL   PRINCIPLES   OF  CHEMISTRY 

number  of  combining  weights  of  the  element  which  enter  the 
compound  in  question. 

Our  choice  of  a  combining  weight  is  limited  by  the  considera- 
tions just  mentioned.  We  must  choose  for  it  the  greatest  value 
which  can  be  chosen  without  contradiction  of  our  principle  of 
integral  coefficients.  This  fundamental  principle  could  evidently 
be  maintained  if  we  assumed  any  rational  fraction  of  this  greatest 
value  as  the  combining  weight  of  the  element,  for  then  all  co- 
efficients would  be  multiples  in  the  corresponding  proportion,  and 
they  would  therefore  still  remain  integral.  For  the  sake  of  sim- 
plicity it  is  necessary  to  add  one  more  condition,  and  this  we  do 
by  choosing  the  greatest  value  as  the  value  for  the  combining 
weight.  In  other  words,  the  combining  weight  is  so  chosen  that 
the  coefficients  necessarily  applied  to  the  element  in  the  molar 
formulae  of  its  compounds  have  no  common  factor. 

It  is  not  possible  to  carry  this  out  for  all  elements,  for  there  are 
several  which  form  no  gaseous  compounds  within  the  limits  of 
our  experimental  knowledge. 

Not  only  the  volumes  of  gas,  but  also  several  other  properties 
of  substances,  are  brought  into  simple  connection  by  the  concept 
of  molar  weight.  These  regularities  open  other  ways  of  making 
a  definite  choice  of  a  combining  weight.  It  has  also  been  found 
that  these  various  principles  all  lead  to  the  same  numerical  re- 
sult, as  far  as  the  choice  of  a  combining  weight  is  concerned.  At 
the  present  time  we  have  a  generally  accepted  system  of  these  con- 
stants, and  the  old  question  about  the  best  choice  of  a  combining 
weight  has  completely  disappeared. 

It  is  customary  at  the  present  time  to  write  most  of  our  chemical 
formulae  so  that  they  indicate,  not  only  the  combining  weight, 
but  also  the  molar  weight  of  the  substances  involved.  To  do  this 
a  mol  of  one  of  the  elements  of  Sec.  173,  whose  gaseous  compounds 
have  double  volume,  must  be  indicated  as  containing  two  com- 
bining weights.  The  chemical  symbol  for  such  an  element  will 
therefore  have  the  form  A2.  The  elements  forming  compounds 


COLLIGATIVE   PROPERTIES  271 

of  fourfold  volume  are  written  B±,  etc.  Chemical  equations 
written  in  this  molar  form  show  immediately  by  definition  the 
volume  relations  in  which  the  substances  should  take  part,  com- 
bine with,  or  form  from  one  another,  as  gases.  Finally,  we  have 
found  that  the  general  chemical  relations  are  most  evidently  and 
logically  represented  by  molar  formulae.  This  method  of  writ- 
ing equations  is  therefore  based  upon  facts  much  more  general 
than  those  representing  gaseous  volumes. 

174.  NUMERICAL  VALUES.  —  Molar  weights  correspond  to 
amounts  of  the  different  gases  occupying  the  same  volume  under 
the  same  conditions  of  temperature  and  pressure.  In  a  strict 
system  of  units  we  would  be  obliged  to  choose  the  molar  quantity 
having  unit  volume  under  unit  temperature  and  unit  pressure. 
Unit  temperature  would  be  1°  in  the  absolute  system  or  —272°  C., 
or  what  amounts  to  the  same  thing,  in  view  of  the  gas  law,  ?fa 
of  the  volume  at  0°,  the  melting  point  of  ice.  Unit  volume  is  1 

cubic  centimetre.    Unit  pressure  in  absolute  measures  is — ,  or 

1  ccm. 

about  the  millionth  of  an  atmosphere.     If  these  values  are  sub- 

PV 

stituted  in  the  gas  equation,  r  =  — ,  amounts  of  the  various  gases 

so  defined  would  give  in  each  case  r  =  l. 

Absolute  units  have,  however,  been  considered  only  in  late 
years,  and  by  an  historical  development  an  entirely  different  and 
much  larger  unit  than  the  one  mentioned  above  has  been  developed 
and  has  come  into  general  use.  This  means,  of  course,  merely 
that  molar  amounts  have  been  increased  in  a  definite  proportion, 
but  it  means  also  that  the  constant  r  of  the  gas  equation  has  a 
different  numerical  value.  At  the  same  time  it  has  remained  equal 
for  molar  amounts  of  the  various  gases. 

We  have  arranged  to  so  choose  our  molar  quantities  that  their 
weight  in  grammes  is  equal  to  the  numerical  value  of  the  molar 
weight,  and  therefore  equal  to  the  sum  of  the  combining  weights 
in  the  molar  formula.  In  order  that  this  may  hold,  the  constant  r 


272  FUNDAMENTAL  PRINCIPLES  OF  CHEMISTRY 

must  be  made  equal  to  82.1,  the  volume  being  measured  in  ccm. 
and  the  pressure  in  atmospheres.* 

If  pressure  is  measured  in  absolute  units,  which  are  about  a 
million  times  smaller,  the  constant  becomes  83.2  x  106. 

By  definition  this  constant  has  the  same  value  for  molar  quan- 
tities of  all  gases  and  vapours.  It  is  therefore  of  very  frequent  occur- 
rence in  chemical  calculations.  The. symbol  R  is  generally  given 
to  it,  and  the  gas  equation  containing  it  has  the  form  PV  =  RT. 
All  calculations  which  involve  pressure,  volume,  density,  and  spe- 
cific volume  of  a  gas  can  be  carried  out  by  the  aid  of  this  equation 
if  the  molecular  weight  of  the  gas  is  known.  If  M  is  this  molecular 

*  The  relations  between  the  unit  of  combining  weight  and  that  of  molar 
weight  have  come  down  to  us  slightly  complicated  because  of  their  remark- 
able historical  development.  Dalton,  who  developed  the  law  of  combining 
weights  on  the  basis  of  a  hypothesis  concerning  the  atomic  structure  of  matter, 
chose  hydrogen  as  his  unit,  because  this  substance  has  the  smallest  atomic 
weight  or  combining  weight.  Because  of  the  low  value  of  the  combining 
weight  of  hydrogen,  compounds  of  this  element  are  difficult  to  analyze,  and 
Dalton  made  errors  of  about  20  per  cent  in  his  determinations.  Berzelius  made 
the  first  exact  determinations  of  combining  weights,  and  he  chose  oxygen  as  his 
standard,  giving  to  it  the  combining  weight  100  instead  of  1 ,  in  order  to  avoid 
using  very  small  numbers.  Later  a  reform  was  undertaken  with  respect  to 
the  rational  factor  of  the  combining  weights  (Sec.  173),  and  this  reform  took 
place  in  connection  with  the  development  of  organic  chemistry  when  it  be- 
came evident  that  it  was  desirable  to  differentiate  the  new  system  as  clearly 
as  possible  from  the  old  one.  The  hydrogen  unit  of  Dalton  was  therefore  in- 
troduced again,  since  the  relation  between  the  combining  weights  of  oxygen 
and  hydrogen  was  thought  to  be  accurately  known.  Later  results  showed, 
however,  that  this  relation  had  been  determined  with  much  less  accuracy  than 
the  relation  of  other  combining  weights,  and  oxygen  was  therefore  made  the 
standard  element  again  for  the  same  reasons  as  led  Berzelius  to  choose  it. 
The  second  time,  however,  the  combining  weight  of  oxygen  was  not  taken 
equal  to  100  as  before,  but  equal  to  16.  This  latter  number  is  the  combining 
weight  of  oxygen  based  on  hydrogen  as  unit,  and  this  ratio  was  assumed  to 
be  correct  for  many  years.  The  relation  is,  however,  more  exactly  1  :  15.87 
or  1.008  :  16.  At  the  present  time  the  combining  weight  of  hydrogen  is  1.008, 
and  if  changes  in  this  number  become  necessary,  this  one  element  alone  will 
be  affected  and  not  the  other  combining  weights.  If  a  change  of  this  sort  were 
to  be  made  in  oxygen  it  would  be  necessary  to  recalculate  all  the  other  com- 
bining weights,  as  they  all  depend  directly  or  indirectly  on  the  analysis  of 
oxygen  compounds.  This  basis  for  the  calculation  of  combining  weights  has 
been  reached  by  international  agreement,  and  this  insures  the  greatest  pos- 
sible unanimity. 


COLLIGATIVE   PROPERTIES  273 

M     MP     M . 

weight  we  have,  for  example,   —  =  — — .     —  is  the  weight  of  a  ccm. 

of  the  gas,  i.  e.  it  is  its  density  under  the  given  conditions  of  tem- 
perature and  pressure.  If  we  make  T=273°  and  P  =  l  atmos- 
phere, we  obtain  the  density  under  normal  conditions. 

By  inserting  the  normal  values  of  pressure  and  temperature  in 

RT 

the  gas  equation  PV  =  RT,  or  V  =  -=j-,  we  obtain  the  molar  volume 

of  all  gases,  that  is,  the  volume  which  is  occupied  by  a  mol  in 
grammes  of  any  gas,  assuming  normal  conditions  for  pressure  and 
temperature.  This  volume  is  22,412  ccm.  The  specific  volume 
of  a  gas  under  the  same  conditions  may  be  found  by  dividing  this 
volume  by  the  molar  weight. 

The  molar  weight  in  grammes  is  of  frequent  use  in  chemical 
calculations,  and  it  is  customary  to  use  the  name  "  mol"  for  it. 
A  solution  of  1  mol  per  litre  indicates  a  solution  containing  a 
number  of  grammes  per  litre  equal  to  the  number  of  units  in  the 
molar  weight  of  the  substance  in  question.  Such  a  solution  is 
called  a  molar  solution,  and  another  solution  containing  ^  of  a 
mol  per  litre  is  called  a  tenth  molar  solution. 

The  name  "  millimol,"  the  thousandth  part  of  a  mpl,  or  a  molar 
weight  in  milligrammes,  is  used  when  small  quantities  of  substance 
and  dilute  solutions  are  required. 

175.  THE  PROPERTIES  OF  DILUTE  SOLUTIONS.  —  Attention 
has  already  been  called  to  the  fact  that  the  equilibrium  between 
a  liquid  and  its  vapour,  or  between  a  liquid  and  its  solid  phase, 
is  changed  when  another  substance  is  dissolved  in  the  liquid. 
This  change  increases  from  zero  as  small  amounts  of  dissolved 
substance  are  added,  and  is  proportional  to  the  content  of  dis- 
solved substance.  All  properties  of  a  solution  are  functions  of  its 
composition,  and  these  effects  and  the  effect  just  mentioned  are 
equal  for  solutions  of  equal  composition. 

The  effects  just  mentioned  are  always  in  a  definite  sense.  The 
vapour  pressure  of  the  solvent  is  always  lowered  by  dissolving  the 
18 


274  FUNDAMENTAL   PRINCIPLES  OF  CHEMISTRY 

other  substance  in  it,  and  the  freezing  point  of  the  solvent  is  also 
lowered  in  the  same  way. 

The  first  statement  holds  for  the  vapour  pressure  of  the  sub- 
stance which  is  present  in  excess,  and  which  we  have  therefore 
called  the  solvent,  and  it  does  not  hold  for  the  total  vapour  pres- 
sure of  the  solution.  In  other  words,  the  partial  pressure  of  the 
solvent  is  decreased.  It  follows  from  this  that  a  corresponding 
statement  cannot  be  made  for  the  boiling  point,  for  the  boiling 
point  of  a  solution  is  higher  than  that  of  the  solvent  only  when 
the  dissolved  substance  is  not  measurably  volatile.  If  the  dis- 
solved substance  has  an  influence  on  the  composition  of  the  vapour, 
the  sense  in  which  the  boiling  point  will  be  changed  depends  upon 
this  composition.  If  only  .a  very  little  of  the  dissolved  substance 
is  present  in  the  vapour,  compared  with  the  amount  in  the  liquid, 
the  boiling  point  will  rise,  but  by  a  less  amount  than  would  be  the 
case  if  none  of  the  dissolved  substance  went  over  into  the  vapour, 
If,  on  the  other  hand,  a  relatively  large  amount  of  the  dissolved 
substance  is  present  in  the  vapour,  as  compared  with  the  amount 
in  the  liquid,  the  boiling  point  will  be  lower  than  that  of  the  sol- 
vent. Finally,  if  the  proportion  is  the  same  in  vapour  and  solution 
no  change  in,  the  boiling  point  will  occur.  Proof  of  these  state- 
ments may  be  drawn  from  a  consideration  of  the  boiling  point 
lines  of  solutions,  especially  where  we  have  a  maximum  or  mini- 
mum boiling  point  (see  Sections  106  and  109). 

Similar  reasoning  holds  for  the  freezing  point.  It  has  just  been 
said  that  ice  *  separates  from  a  solution  at  a  lower  temperature 
than  from  the  solvent.  This  holds,  however,  only  under  the  as- 
sumption (usually  fulfilled)  that  the  ice  itself  is  the  pure  substance. 
If  a  solid  solution  is  formed,  a  set  of  conclusions  precisely  similar 
to  those  drawn  for  boiling  points  will  hold.  The  freezing  point 
sinks  when  less  of  the  solid  substance  is  present  in  the  solid  solu- 
tion than  in  the  liquid  one.  If  the  inverse  is  true,  the  freezing 

*  By  ice  is  meant  in  general  a  hylotropic  solid  phase  corresponding  to  a 
liquid. 


COLLIGATIVE   PROPERTIES  275 

point  rises,  and  it  will  remain  unchanged  if  the  composition  of 
both  is  the  same.  Solid  solutions  occur  only  rarely,  and  we  will 
therefore  leave  out  this  possibility  except  in  cases  where  it  is  spe- 
cially mentioned. 

176.  MOLAR  LOWERING  OF  THE  VAPOUR  PRESSURE.  —  All 
dissolved  substances  lower  the  vapour  pressure,  and  within  fairly 
wide  limits  they  do  so  in  proportion  to  the  content  of  dissolved 
substance  in  the  solution.  The  question  therefore  arises  what 
property  determines  the  amount  of  this  lowering  for  a  given  con- 
tent of  dissolved  substance,  or,  it  might  be  asked,  what  amounts 
produce  the  same  lowering.  The  answer  which  experiment  has 
taught  us  is  that  equimolar  solutions  correspond  to  the  same  lowering 
of  vapour  pressure. 

Equimolar  solutions  have  been  explained  in  the  previous  para- 
graph to  be  those  which  contain  an  equal  number  of  mols  of  the 
dissolved  substance  in  a  given  amount  of  solvent,  or,  what  amounts 
to  the  same  thing,  they  are  solutions  which  contain  an  equal 
amount  of  solvent  to  a  mol  of  various  substances. 

It  follows  that  a  definite  parallelism  exists  between  the  gase- 
ous state  and  the  state  of  a  dilute  solution  with  reference  to  the 
dissolved  substance.  Equal  volumes  of  different  gases  contain 
amounts  which  are  in  simple  relations  to  the  combining  weights. 
In  the  same  way  an  equal  lowering  of  the  vapour  pressure  corre- 
sponds to  amounts  of  different  substances  which  have  the  same 
simple  relation  to  the  combining  weights.  The  amounts  deter- 
mined in  these  two  ways  are,  in  the  majority  of  cases,  propor- 
tional to  one  another  (or  equal  to  one  another  if  units  are  properly 
chosen).  The  determination  of  molar  weights,  which  has  so  far  been 
possible  only  in  the  gaseous  state,  can  now  be  extended  to  apply 
to  all  substances  which  can  be  dissolved  in  any  volatile  solvent. 

Properties  like  this,  which  have  the  same  value  for  equimolar 
amounts  of  different  substances,  are  called  colligative  properties, 
and  there  are  several  of  these  beside  gas  volume  and  lowering  of 
vapour  pressure. 


276  FUNDAMENTAL   PRINCIPLES  OF  CHEMISTRY 

177.  OSMOTIC  PRESSURE. — The  relation  between  the  vapour 
pressure  of  a  solution  and  that  of  the  pure  solvent  depends,  as  do 
the  other  colligative  properties  which  belong  to  solutions,  on 
energy  changes  which  become  active  when  solutions  are  made. 
It  has  already  been  mentioned  that  a  solution  which  has  once  been 
formed  does  not  separate  of  its  own  accord  into  its  original  con- 
stituents without  the  expenditure  of  external  work.  It  follows 
that  when  solutions  are  produced  from  their  constituents  work 
is  given  out  which  can  be  made  useful  by  proper  experimental 
arrangement.  The  same  holds  true  when  a  gas  is  produced  by 
any  process.  If  P  is  the  pressure  under  which  it  is  evolved,  and 
V  the  volume  which  it  occupies,  then,  if  the  gas  is  to  form,  the 
pressure  P  must  be  overcome  through  the  volume  V.  The  work 
to  be  done  is  the  product  of  pressure  and  volume,  and  is  therefore 
PV.  If  a  mol  of  each  gas  is  produced,  the  numerical  value  for 
the  work  PV  will  be  the  same  for  each  gas,  and  it  will  be  PV =  RT. 
This  work  is  independent  of  the  pressure  P,  for  since  pressure  is 
inversely  proportional  to  volume  the  product  PV  always  has  the 
same  value  no  matter  what  the  pressure  may  be.  It  will  be  noticed 
that  this  work  is  also  proportional  to  the  absolute  temperature  T, 
as  will  be  seen  in  the  formula.  Conversely  an  amount  of  work 
PV  must  be  expended  when  a  gas  disappears,  that  is,  whenever 
it  is  changed  into  a  solid  or  a  liquid.  The  relation  expressed  as 
above,  and  including  the  concept  of  a  mol,  declares  in  other  words 
that  molar  quantities  of  different  gases  are  quantities  such  that 
the  same  amount  of  external  work  or  volume  energy  is  given  out 
during  their  formation  (assuming  the  same  temperature  in  each 
case).  These  same  quantities  of  different  gases  are  also  in  simple 
proportion  to  their  combining  weights. 

Similar  relations  hold  for  solutions.  If  we  permit  a  layer  of 
pure  solvent  to  flow  over  a  solution  the  process  of  diffusion  begins 
immediately.  The  dissolved  substance  spreads  of  its  own  accord 
into  the  solvent,  and  this  continues  until  the  concentration  is  equal 
in  all  parts  of  the  solution.  In  the  same  way  a  gas  spreads  out  into 


COLLIGATIVE   PROPERTIES  277 

a  vacant  space,  and  this  process  only  stops  when  the  concentra- 
tion of  the  gas  is  the  same  throughout  the  entire  space.  In  the 
two  cases  we  mean  precisely  the  same  thing  by  concentration, 
that  is,  the  amount  of  the  substance  in  question  contained  in  the 
unit  of  volume,  whether  a  dissolved  substance  or  gas.  Here  con- 
centration by  weight  must  be  kept  separate  from  molar  concen- 
tration; the  former  is  given  by  the  weight  in  grammes  which  is 
contained  in  a  cubic  centimetre,  the  latter  by  the  number  of  mols 
in  the  same  volume.  In  gases  the  definition  of  concentration  by 
weight  is  synonymous  with  density.  Among  solutions  concentra- 
tion by  weight  gives  the  partial  density  of  the  dissolved  substance 
in  the  volume  occupied  by  the  solution. 

Among  solutions  the  pure  solvent  plays  the  same  part  that  a 
vacuum  plays  for  a  gas. 

If  a  gas  is  bounded  by  empty  space  it  can  be  prevented  from 
spreading  into  it  by  interposing  a  solid  partition.  This  partition 
will  experience  a  pressure  which  depends  upon  the  volume  and 
the  temperature  of  the  gas.  If  these  two  factors  are  kept  constant, 
molar  quantities  of  various  gases  exercise  the  same  pressure,  and 


the  numerical  value  of  this  pressure  is  given  by  P=  —  . 

If  a  solution  is  bounded  by  a  pure  solvent,  the  dissolved  sub- 
stance can  be  prevented  from  spreading  into  it  by  interposing  a 
diaphragm.  If  this  diaphragm  is  to  experience  a  measurable  pres- 
sure it  must  be  able  to  move  in  such  a  way  that  the  dissolved  sub- 
stance can  assume  a  larger  volume,  and  in  order  that  this  should 
take  place  the  dissolved  substance  must  spread  into  a  larger  volume 
of  the  solvent.  The  partition  must  therefore  be  able  to  move 
through  the  solvent  unhindered,  that  is  to  say,  it  must  permit  the 
solvent  to  pass  through  it,  but  not  the  dissolved  substance.  Such 
partitions  may  be  found  in  plant  cells.  In  a  living  state  certain 
substances  remain  dissolved  in  the  cell  liquid,  and  these  substances 
cannot  leave  the  cell,  even  though  it  is  in  contact  with  pure  water. 
The  water  itself  passes  through  the  cell  wall  without  hindrance. 


278  FUNDAMENTAL  PRINCIPLES  OF  CHEMISTRY 

It  is  also  experimentally  possible  to  produce  such  walls  artificially, 
at  least  for  certain  substances.  Such  membranes  are  said  to  be 
semi-permeable,  and  they  play  the  same  part  toward  dissolved  sub- 
stances that  solid  walls  would  for  gases.  All  the  operations  which 
can  be  carried  out  for  gases  by  means  of  solid  walls  can  be  repeated 
in  solutions  with  semi-permeable  ones. 

It  has  been  shown  experimentally  that  the  pressure  experienced 
by  such  a  semi-permeable  membrane,  when  placed  between  solu- 
tions of  different  concentration,  can  be  described  by  the  same  laws 
as  those  which  describe  pressure  in  gases.  The  pressure  of  a 
solution  on  such  a  semi-permeable  membrane  is  called  the  osmotic 
pressure.  Van't  Hoff  showed  that  this  osmotic  pressure  is  repre- 
sented by  the  gas  law  PV  =  RT.  The  osmotic  pressure  is  inversely 
proportional  to  the  volume,  or,  what  amounts  to  the  same  thing, 
directly  proportional  to  concentration  or  partial  density.  It  is 
furthermore  proportional  to  the  absolute  temperature,  and,  finally, 
under  given  conditions  of  volume  and  pressure,  its  numerical  value 
is  the  same  as  that  of  the  gaseous  pressure  which  would  be  ex- 
hibited by  the  same  substance  if  it  occupied  the  same  space  at  the 
same  temperature  in  the  form  of  a  gas.  It  follows  from  this  that 
the  constant  R  has  the  same  value  for  equal  molar  amounts  of  dis- 
solved substances  and  that  this  value  is  the  same  as  for  gases.  If 
the  pressure  is  measured  in  atmospheres,  the  equation  PV  =  82.lT 
holds  for  the  osmotic  pressure  of  dissolved  substances. 

A  dissolved  substance  therefore  gives  out  or  takes  in  work  during 
a  change  of  concentration  just  as  a  gas  does  during  a  change  of 
pressure.  It  is,  in  general,  possible  to  produce  a  change  in  the 
density  of  a  gas  (aside  from  the  effect  of  temperature)  only  by  the 
use  of  some  mechanical  means,  such  as  a  cylinder  and  piston. 
Changes  in  the  concentration  of  solutions  can,  however,  be  brought 
about  by  any  process  by  which  solvent  can  be  added  or  withdrawn. 
A  semi-permeable  membrane  affords  one  means.  Evaporating 
the  solution  so  that  the  solvent  escapes  is  another.  A  third  con- 
sists in  separating  the  solvent  in  the  form  of  a  solid  phase,  by  par- 


COLLIGATIVE  PROPERTIES  279 

tial  freezing,  for  example.  From  this  point  of  view  the  necessity 
of  the  relation  explained  in  Sec.  175  will  be  evident.  A  rise  in 
boiling  point,  corresponding  to  an  increased  amount  of  work  ex- 
pended on  the  solution,  only  appears  when  the  vapour  which  sepa- 
rates contains  less  of  the  dissolved  substance  than  the  solution  itself. 
If  it  contains  the  same  amount  no  expenditure  of  work  is  necessary 
for  the  separation  and  therefore  no  change  in  the  boiling  point 
takes  place.  If  the  vapour  contains  more  of  the  dissolved  substance 
the  opposite  effect  is  to  be  expected.  The  solution  is  diluted  by 
boiling,  and  the  boiling  point  is  lowered  by  a  corresponding 
amount. 

Corresponding  changes  in  the  freezing  point  are  directly  con- 
nected with  the  boiling  point  changes  just  described  by  the  rela- 
tions which  exist  between  the  vapour  pressure  of  the  solution  and 
that  of  ice.  They  can  therefore  be  deduced  directly  from  them,  as 
will  be  shown  immediately. 

178.  NUMERICAL  RELATIONS.  —  The  conclusions  just  reached 
can  be  expressed  in  formulae  by  the  application  of  a  principle 
which  we  have  frequently  used.  That  which  is  in  equilibrium  in 
one  sense  is  in  equilibrium  in  every  sense.  Let  us  imagine  a  solu- 
tion separated  from  a  pure  solvent  by  a  semi-permeable  membrane 
and  held  in  equilibrium  with  it  by  the  application  of  a  hydrostatic 
pressure  equal  to  the  osmotic  pressure.  If  such  a  system  is  in 
equilibrium  we  may  be  sure  that  it  is  in  equilibrium  for  any  process 
whatever,  and,  what  especially  interests  us,  for  any  process  by 
which  the  maintenance  of  a  definite  concentration  in  the  solution 
might  be  influenced.  In  other  words,  the  determining  quantities 
on  which  such  a  change  would  depend  must  have  values  such  that 
the  change  is  impossible. 

Fig.  64  represents  a  vessel  of  pure  solvent,  and  standing  in  it 
a  cylinder  containing  a  definite  solution  and  closed  at  the  bottom 
with  a  semi-permeable  membrane.  The  height  of  the  cylinder  is 
to  be  so  chosen  that  its  hydrostatic  pressure  is  just  sufficient  to 
maintain  equilibrium  against  the  osmotic  pressure  on  the  semi- 


280 


FUNDAMENTAL  PRINCIPLES  OF  CHEMISTRY 


-fl 


FIG.  64. 


permeable  membrane.    The  system  is  then  in  equilibrium  as  far  as 
osmotic  pressure  is  concerned,  that  is  to  say,  solvent  will  not  leave 
the  solution  and  pass  out  through  the  semi-permeable  membrane, 
^^_^^  producing    a    more     concentrated 

jf         "*^\  solution,  nor  can  solvent  enter  the 

'  "  cylinder,    increasing   the   height  of 

the  liquid  column  and  making  the 
solution  more  dilute. 

One  possibility,  however,  still 
remains  open.  The  solution  may 
become  more  dilute  or  more  concen- 
trated by  the  transport  of  solvent 
through  the  vapour.  If  the  solvent 

evaporated  at  the  open  end  of  the 

cylinder  and  condensed  in  the  dish 
below  the  solution  might  become 
more  concentrated,  and  vice  versa.  The  principle  we  have 
just  stated  demands  that  both  of  these  possibilities  should  be 
excluded. 

It  might  be  reasoned  at  first  sight  that  the  vapour  pressure  of 
the  solution  must  be  the  same  as  that  of  the  solvent,  and  that 
therefore  no  effect  should  be  produced  on  the  vapour  pressure  of 
the  volatile  liquid  by  dissolving  a  substance  in  it.  This  conclusion 
contradicts  experience,  for  it  has  been  known  for  a  century  and 
more  that  the  boiling  point  of  water  is  raised  when  a  salt  is  dissolved 
in  it.  In  making  this  first  conclusion  we  have  overlooked  the  fact 
that  the  two  vessels  containing  the  same  liquid,  but  having  different 
levels,  are  by  no  means  in  equilibrium.  If  the  two  are  connected 
by  a  tube  the  upper  liquid  will  flow  into  the  lower  vessel  by  gravity, 
and  if  they  are  connected  merely  by  a  common  atmosphere  con- 
taining vapour  the  upper  liquid  will  distil  into  the  lower  one  for 
the  same  reason.  For  anything  which  is  not  in  equilibrium  in  one 
sense  cannot  be  in  equilibrium  in  any  sense. 

As  a  matter  of  fact  there  exists  in  this  case  a  difference  of  pres- 


COLLIGATIVE  PROPERTIES  281 

sure  between  the  upper  and  lower  free  surfaces  of  the  liquid,  and  this 
difference  is  equal  to  the  hydrostatic  pressure  of  the  vapour  which 
fills  the  space.  If  then  equilibrium  is  to  exist  in  our  apparatus  with 
the  semi-permeable  membrane  and  the  liquid  column,  the  vapour 
pressure  of  the  solution  must  be  less  than  that  of  the  pure  solvent 
by  an  amount  equal  to  the  hydrostatic  pressure  of  a  column  of  va- 
pour as  long  as  the  column  of  liquid  in  the  cylinder.  The  lowering 
of  the  vapour  pressure  stands  in  the  same  relation  to  the  osmotic 
pressure  as  the  density  of  the  vapour  does  to  that  of  the  liquid. 

If  we  wish  to  express  this  in  a  formula,  the  height  of  the  liquid 
and  vapour  column  may  be  called  h  and  the  density  of  the  liquid  D. 
The  hydrostatic  pressure  of  the  liquid,  which  is  equal  to  the  osmotic 
pressure  PQ,  will  have  the  value  PQ  —  hD.  The  osmotic  pressure 
has  the  same  value  as  that  of  the  gas  pressure  which  would  be 
experienced  by  the  dissolved  substance  if  it  were  present  in  gaseous 
form  and  with  the  same  molar  weight  occupying  the  same  volume 
as  the  solution.  This  pressure  is  given  by  the  gas  equation  P^V^ 


RT 

We  therefore  have  PQ  =  -=-  .     In  this  expression  we  must  replace 

the  volume  V  by  a  proper  value  for  the  solution.  Suppose  the 
solution  contains  N  mols  of  the  solvent  to  each  mol  of  the  dis- 
solved substance,  and  that  M  is  the  molar  weight  of  the  solvent, 
then  the  weight  of  solvent  for  each  mol  of  dissolved  substance  is 

NM 
NM  and  the  volume  is  —  —  -  .    Let  us  assume  that  the  solution  is  so 

dilute  that  its  density  and  volume  are  equal  to  that  of  the  pure 

RTD 

solvent.    We  obtain  for  osmotic  pressure  the  value  PQ  =    AT,,,  and 

RT 

since  P0  =  hD  the  height  of  the  liquid  column  h  = 


We  can  now  make  use  of  this  value  to  calculate  the  hydrostatic 
pressure  of  the  vapour  column.  This  pressure  is  kd,  where  d  is  the 
density  of  the  vapour,  and  it  represents  the  lowering  of  the  vapour 
pressure  produced  in  the  solvent  by  the  solution  of  the  dissolved 


282  FUNDAMENTAL  PRINCIPLES  OF  CHEMISTRY 

substance.  Let  us  designate  this  lowering  by  A,  and  we  then  have 
A  =  hd.  To  find  the  unknown  d  we  may  again  make  use  of  the 
gas  equation  as  applied  to  the  vapour.  In  the  expression  pv=RT 
p  is  the  vapour  pressure  of  the  pure  solvent  and  v  the  volume  of  a 
mol  of  the  pure  solvent  at  the  pressure  p.  The  density  d  is  equal 
to  the  weight  of  a  mol  M  of  the  solvent  divided  by  the  volume,  and 

since  v  =  -  ,  d  =  =—  .     Multiplying  this  value  by  the  value  of  h, 


h  =          ,  we  obtain  A  =  hd  =  -     ,  or       =  N. 


It  will  be  seen  that  our  final  formula  contains  neither  R,  T,  nor 
M,  and  that  it  is  therefore  exceedingly  simple.  The  number  of 
mols  of  solvent  for  each  mol  of  dissolved  substance  is  equal  to 
the  ratio  of  the  vapour  pressure  of  the  solvent  to  the  lowering  of 

vapour  pressure  in  the  solution.     Calling  —  the  molar  concentra- 

A 
tion  and  —  the  relative  lowering  of  vapour  pressure,  we  have  the 

simple  statement:  the  relative  lowering  of  the  vapour  pressure  is 
equal  to  the  molecular  concentration. 

179.  INTERPRETATION.  —  The  above  result  is  remarkable  for 
its  simplicity.  It  contains  neither  the  temperature  nor  any  factor 
involving  the  nature  of  the  substances  concerned.  The  change  in 
vapour  pressure  is  referred  exclusively  to  the  ratio  between  the 
number  of  mols  of  dissolved  substance  to  the  number  of  mols  of 
solvent. 

It  is  easy  to  see  why  the  effect  of  temperature  disappears.  A 
rise  in  temperature  corresponds  to  an  increased  osmotic  pressure, 
since  the  latter  is  proportional  to  the  absolute  temperature,  and 
we  may  assume  that  the  volume  of  the  solution  remains  constant 
because  of  the  small  coefficient  of  expansion  which  is  characteristic 
of  liquids.  The  density  of  the  vapour  will,  however,  decrease  in 
direct  proportion  to  the  absolute  temperature  if  the  pressure  re- 
mains the  same.  The  column  of  vapour  which  determines  the 


COLLIGATIVE    PROPERTIES  283 

lowering  of  the  vapour  pressure  will  therefore  be  higher  at  higher 
temperatures,  but  at  the  same  time  it  will  have  a  correspondingly 
lower  density.  The  hydrostatic  pressure  will  remain  constant,  and 
the  effect  of  temperature  disappears.  The  vapour  pressure  does 
not,  however,  remain  the  same,  since  it  increases  in  accordance 
with  laws  which  depend  upon  the  nature  of  the  liquid  ;  but  the 
hydrostatic  pressure  of  the  column  of  vapour  increases  in  the  same 
proportion  as  the  density  of  the  vapour,  and  it  has  therefore  under 
all  circumstances  a  value  which  is  the  same  fraction  of  the  vapour 
pressure.  It  follows  from  this  that,  while  the  absolute  lowering  of 
the  vapour  pressure  is  not  independent  of  temperature,  the  propor- 
tional lowering  of  the  vapour  pressure  is  quite  independent  of  it, 
and  this  fact  is  expressed  by  the  formula.  The  gas  equation  applies 
to  both  parts  of  the  relation,  the  osmotic  pressure,  and  the  condi- 
tion of  the  vapour  in  the  vessel.  Factors  which  depend  upon  it 
cancel  one  another,  and  this  leads  to  great  simplicity  in  the  result. 
The  same  reasons  determine  the  fact  that  the  molar  proportion 
determines  the  relative  lowering  of  the  vapour  pressure.  The 


osmotic  column  h  =  is  affected  by  the  molecular  weight  M 

and  the  temperature  T  in  the  opposite  sense  from  the  effect  due 

to  the  density  of  the  vapour  d  =  —  ^  .     These  two  effects  therefore 

HI 

cancel  one  another  in  the  product,  and  there  remains  only  the 
relation  between  molar  proportion,  vapour  pressure,  and  lowering 
of  vapour  pressure,  as  given  above. 

The  osmotic  pressure  always  has  a  positive  value,  and  the  column 
of  liquid  in  this  apparatus  can  only  be  raised  and  never  lowered  by 
its  action.  It  follows  necessarily  that  dissolved  substances  which 
exert  an  osmotic  pressure  can  only  decrease  the  vapour  pressure 
of  the  solvent,  and  can  never  under  any  circumstances  increase  it. 
We  know  of  some  solutions  which  cannot  be  distinguished  from 
ordinary  solutions  so  far  as  their  mechanical  and  optical  proper- 
ties are  concerned,  but  which  exhibit  no  osmotic  pressure.  Solu- 


284 


FUNDAMENTAL   PRINCIPLES   OF  CHEMISTRY 


tions  of  this  kind  are  called  colloidal  solutions,  and  they  have  no 
measurable  effect  on  the  vapour  pressure  of  the  solvent. 

180.  THE  EFFECT  ON  FREEZING  POINT.  —  The  laws  which 
describe  the  lowering  of  the  freezing  point  can  be  deduced  most 
directly  by  considering  the  vapour  pressure  of  solution  and  ice. 
The  same  principle  which  enables  us  to  deduce  the  laws  describ- 
ing the  lowering  of  vapour  pressure  from  those  of  osmotic  pressure 
leads  to  the  conclusion  that  ice  and  solution  can  only  be  in  equilib- 
rium at  a  temperature  such  that  their  vapour  pressures  are  equal ; 
for  if  the  vapour  pressures  are  different,  solvent  distils  over  to  form 
more  ice  and  the  concentration  of  the  solution  increases,  or  the 
reverse  process  takes  place  and  ice  distils  into  the  solution,  de- 
creasing the  concentration  of  the  latter. 

It  is  evident  first  of  all  that  the  solution  cannot  be  in  equilibrium 
with  ice  at  the  melting  point  of  the  pure  solvent,  for  at  that  point 

the  solid  phase  has  the  same 
vapour  pressure  as  the  liquid, 
while  the  solution  certainly  has 
a  lower  vapour  pressure.  The 
difference  between  the  vapour 
pressure  of  the  solid  and  liquid 
phases  is  such  that  the  vapour 
pressure  of  the  ice  is  greater 
above  the  melting  point  and 
smaller  below  this  point  than 
that  of  the  liquid  phase.  The 

vapour  pressure  of  ice  and  solution  can  therefore  be  equal  only 
at  a  point  which  lies  below  the  melting  point  of  the  pure  solvent. 
In  Fig.  65  the  vapour  pressure  line  of  the  pure  solvent  is  labelled 
"  water,"  and  the  vapour  pressure  line  of  the  hylotropic  solid 
phase  is  indicated  by  the  line  marked  "ice."  At  the  melting 
point  /  the  two  vapour  pressures  are  equal,  and  below  this  point  the 
vapour  pressure  of  ice  lies  below  that  of  the  water.  For  the  small 
differences  which  need  to  be  considered  the  vapour  pressure  line 


FIG.  65. 


COLLIGATIVE   PROPERTIES  285 

of  the  solution  is  approximately  parallel  to  that  of  the  solvent,  in 
agreement  with  the  laws  developed  in  the  previous  paragraph,  and 
the  distance  between  these  two  lines  is  proportional  to  the  molar 
concentration  of  the  solution. 

The  freezing  point  of  the  solution  is  given  as  the  point  where 
the  vapour  pressure  curves  for  solution  and  ice  cut  each  other, 
and  this  follows  from  the  general  conditions  of  equilibrium.  It 
will  be  noticed  that  it  lies  at  a  lower  temperature  than  the  freezing 
point  of  the  pure  solvent.  If  the  vapour  pressure  lines  are  taken 
as  straight  lines  throughout  the  region  in  question,  and  if  we  as- 
sume that  the  lines  for  water  and  solution  are  parallel,  it  is  evident 
that  the  lowering  of  the  freezing  point  is  proportional  to  the  lower- 
ing of  vapour  pressure.  Their  numerical  ratio  depends  upon  the 
angle  at  which  the  curves  for  ice  and  water  cross. 

It  follows  immediately  that  equimolar  solutions  of  various  sub- 
stances in  the  same  solvent  must  cause  the  same  lowering  of  the 
freezing  point,  and  experience  proved  this  long  before  any  relation 
to  the  laws  of  osmotic  pressure  was  recognised.  It  is  evident  also 
that  the  lowering  of  the  freezing  point  will  be  proportional  to  the 
molar  concentration,  and  since  the  latter  is  proportional  to  the 
concentration  by  weight,  the  lowering  of  the  freezing  point  must 
also  be  in  the  same  proportion. 

This  principle  has  been  known  for  more  than  a  century  as  an 
experimental  fact.  In  various  solvents  the  lowering  of  the  freezing 
point  must  depend  upon  factors  which  determine  the  angle  between 
the  vapour  pressure  curves  of  ice  and  water.  The  development  of 
the  latter  relation  will  not  be  taken  up  in  this  book,  and  its  appli- 
cation will  therefore  not  be  considered.  It  may  be  stated,  however, 
that  this  angle  (or  rather  its  tangent)  increases  proportionately 
with  the  latent  heat  of  melting  of  the  solid  phase.  It  follows  that 
the  lowering  of  the  freezing  point  will  vary  inversely  as  the  heat 
of  fusion,  for  the  point  of  contact  of  the  two  curves  will  be  farther 
from  the  melting  point  as  the  angle  between  them  is  made  smaller 
and  smaller.  Experiment  confirms  this  result  also. 


286  FUNDAMENTAL  PRINCIPLES  OF   CHEMISTRY 

It  may  be  asked  in  conclusion  why  the  change  in  freezing  point 
cannot  be  stated  with  the  same  simplicity  as  the  lowering  of  the 
vapour  pressure.  The  reason  for  this  is  that  comparisons  of  the 
lowering  of  vapour  pressures  are  made  at  constant  temperature 
while  the  effect  of  the  freezing  point  involves  the  use  of  different 
temperatures.  It  may  also  be  asked  what  relation  exists  between 
the  lowering  of  vapour  pressure  and  the  corresponding  rise  of  the 
boiling  point,  since  in  this  case  also  differences  of  temperature 
enter.  A  precisely  similar  set  of  conclusions  leads  in  this  case  to 
a  formula  exactly  similar  to  that  for  the  lowering  of  the  freezing 
point. 

181.  THE  IMPORTANCE  OF  THE  SOLUTION  LAWS.  —  The  solu- 
tion laws  enable  us  to  determine  the  quantities  of  energy  which 
correspond  to  the  formation  of  solutions  and  also  those  which 
correspond  to  any  change  of  concentration  in  solutions.  They 
offer  us  the  means  of  setting  up  conditions  of  equilibrium  for  all 
processes  in  which  changes  of  concentration  take  place.  They 
give  us  therefore  a  foundation  for  the  study  of  chemical  equilibrium 
in  solution,  for  the  theory  of  the  electromotive  force  of  a  voltaic 
cell,  etc.  We  shall  not,  however,  take  up  these  applications  at 
present.  The  solution  laws  enable  us  to  reach  a  theoretically 
complete  solution  of  another  problem  which  has  already  been 
mentioned.  In  Sec.  173  it  was  stated  that  the  choice  of  combin- 
ing weights  from  among  the  possible  values,  with  the  aid  of  molar 
weights  and  the  rule  that  no  fractional  combining  weights  should 
appear  in  the  molar  weights,  is  limited  to  a  considerable  degree. 
Gaseous  compounds  of  many  of  the  elements  are  either  not  known 
or  exist  under  conditions  which  make  measurement  impossible, 
but  with  the  aid  of  the  laws  of  solutions  molar  weights  can  be 
determined  for  all  soluble  substances.  Scarcely  a  substance  exists 
for  which  a  solvent  cannot  be  found,  and  this  means  that  it  is 
generally  possible  to  determine  the  molar  weights  of  all  the  com- 
pounds of  the  elements. 

The  probability  that  substances  exist  whose  molar  weight  con- 


COLLIGATIVE   PROPERTIES  287 

tains  only  a  fraction  of  the  combining  weight  of  one  of  its  elements 
is  therefore  exceedingly  small,  and  the  combining  weights  now 
in  use,  which  are  based  upon  these  extended  determinations,  must 
be  considered  as  being  sufficiently  definite  for  all  purposes. 

If  this  conclusion  is  to  be  used  with  complete  scientific  certainty, 
the  question  as  to  the  relation  between  molar  weights  determined 
from  the  properties  of  solutions  and  those  calculated  from  the 
properties  of  gases  remains  to  be  answered.  The  reasoning  of 
Sec.  178  is  applicable  here.  It  was  shown  at  that  point  that  the 
law  of  the  lowering  of  vapour  pressure  (which  was  originally  an 
experimental  fact)  assumes  on  the  one  hand  the  law  of  gas  pres- 
sure, and  on  the  other  hand  that  of  osmotic  pressure.  These  two 
laws  are  therefore  supported  by  the  experimental  confirmation 
of  the  law  of  the  lowering  of  vapour  pressure.  In  the  majority 
of  cases  experiment  has  confirmed  the  fact  that  the  same  molar 
weights  are  found  whether  they  are  determined  from  the  gas 
pressure  or  the  osmotic  pressure.  In  individual  cases  larger  values 
have  been  found  for  molar  weights  in  solution  than  for  the  same 
substances  in  the  state  of  vapour,  but  in  these  cases  it  can  be  shown 
with  certainty  that  in  the  particular  solutions  in  question  multiples 
of  the  other  molar  weight  are  active.  The  nature  of  the  solvent 
is  an  important  factor.  The  same  substance  dissolved  in  various 
solvents  is  comparable  with  a  substance  under  investigation  at 
various  temperatures,  and  even  among  the  elements  there  are  a 
few  whose  molar  weight  in  the  gaseous  state  is  different  at  different 
temperatures. 

Another  special  case  where  the  molar  weight  is  too  small  in 
solutions  will  be  considered  more  at  length  in  the  chapter  on  ions. 

182.  COLLIGATIVE  PROPERTIES.  J—  Those  properties  which  are 
related  to  molar  quantities  are  called  colligative  properties,  and 
they  have  equal  values  for  equimolar  amounts  of  various  sub- 
stances, wholly  independent  of  the  other  properties  of  the  sub- 
stances involved.  Among  these  we  find  first  of  all  the  volume  of 
gases,  or,  in  more  general  terms,  the  R  value  in  the  equation  of 


288  FUNDAMENTAL   PRINCIPLES  OF  CHEMISTRY 

condition  for  a  gas,  and  the  corresponding  value  in  the  equation 
for  solutions.  A  second  set  of  properties,  including  the  lowering 
of  the  freezing  point,  lowering  of  the  vapour  pressure,  and  rise  of 
the  boiling  point,  all  of  which  are  determined  by  the  equation  of 
condition  for  solutions,  also  come  under  this  head.  The  question 
arises  whether  other  properties  of  the  same  sort  exist,  and  if  so 
what  relation  they  exhibit  to  those  already  mentioned. 

It  was  shown  in  Sec.  169  that  many  properties  assume  values 
which  are  either  equal  or  in  simple  rational  proportion  if  they 
are  based  upon  the  combining  weight  of  the  substance  in  ques- 
tion. These  will  only  be  colligative  properties  in  the  sense  of  our 
definition  if  the  rational  factors,  which  must  be  used  to  make  the 
values  of  the  properties  based  on  the  combining  weights  equal, 
are  the  same  for  all  properties  (as  they  are  for  gases  and  solu- 
tions). This  is  not  the  case  in  general.  Equal  amounts  of 
electricity  do  not  appear  during  electrolysis  with  equal  molar 
amounts  of  various  substances.  The  rational  factors  in  this  case 
are  wholly  different.  It  is  therefore  necessary  to  introduce  another 
idea,  that  of  chemical  equivalents.  In  the  same  way  equal  heat 
capacities  correspond  among  the  elements  to  amounts  which  are 
in  the  proportion  of  the  combining  weights.  Among  compounds 
heat  capacities  are  proportional  to  the  number  of  combining 
weights  of  the  element  in  the  compound. 

One  other  property,  which  is  called  molar  surface  energy,  is, 
however,  very  nearly  a  colligative  one.  This  holds  for  pure  liquids, 
and  we  can  determine  molar  composition  with  its  aid  if  we  assume 
that  it  is  a  colligative  property.  This  assumption  is  supported  by 
the  far-reaching  agreement  between  molar  weights  determined  by 
this  and  the  other  methods.  Even  the  singularities  which  corre- 
spond to  differences  of  molar  weight  in  solutions  in  various  solvents 
find  their  corresponding  expression  in  differences  in  molar  surface 
energy.  The  molar  concept  has  so  far  attained  no  importance 
among  solids  in  the  sense  in  which  it  is  here  used.  No  satisfactory 
method  has  yet  been  developed  for  measuring  the  amount  of 


COLLIGATIVE   PROPERTIES  289 

work  corresponding  to  the  formation  of  solid  solutions  or  to  changes 
in  them.  There  is,  however,  no  fundamental  reason  why  such  a 
process  should  not  be  discovered,  and  if  it  is,  all  of  our  reasoning 
would  be  applicable  to  solid  solutions.  It  would  also  be  possible 
to  make  use  of  the  same  set  of  relations  for  pure  solids  if  colliga- 
tive  properties  were  known  among  them. 

No  extension  of  the  law  of  the  equality  of  molar  surface  energy 
(at  constant  temperature)  to  include  solid  substances  has  yet 
been  made,  because  measurement  of  surface  tension  among  solids 
is  still  accompanied  by  very  great  difficulties.  Other  difficulties 
arising  from  the  crystalline  structure  must  also  be  overcome.* 

*  It  is  necessary  to  differentiate  carefully  between  conclusions  like  these 
and  hypothetical  investigations  of  so-called  molecular  size  among  gaseous, 
liquid,  and  solid  substances.  By  this  is  meant  the  size  of  the  hypothetical 
molecules,  which  are  denned  as  the  smallest  amounts  of  substances  which 
can  exist  independently.  Various  considerations,  all  of  which  contain  a  larger 
or  smaller  number  of  arbitrary  assumptions,  or  other  uncertainties,  have  been 
applied  with  the  hope  of  reaching  conclusions  about  molecular  sizes.  Such 
processes  lead  to  the  assumption  that  the  weights  of  the  molecules  must  be 
proportional  to  the  molar  weights,  as  calculated  from  the  laws  for  gases  and 
solutions. 


19 


CHAPTER  IX 
REACTION   VELOCITY  AND   EQUILIBRIUM 

183.  REACTION  VELOCITY.  —  A  definite  time  may  be  said  to 
be  a  function  of  every  physical  process.  So  far  in  our  discussion 
we  have  made  the  assumption  that  time  has  no  effect  on  the  factors 
considered.  This  includes  another  assumption,  which  is  that  the 
phenomena  in  which  time  is  a  factor  have  already  taken  place, 
and  that  we  have  arrived  at  a  condition  which  is  no  longer  variable 
with  time.  Every  system,  so  far  as  we  know,  tends  toward  this 
condition.  Every  unequalized  difference  in  energy  is  a  reason 
for  something  happening,  —  the  differences  tend  to  equalize  each 
other,  and  such  a  change  is  necessarily  coupled  with  changes  in 
the  condition  of  the  system  considered.  Changes  in  the  amount 
of  energy  present,  by  a  decrease  in  such  differences,  determine 
everything  that  happens  in  the  light  of  final  analysis,  or  at  any 
rate  they  determine  something  which  is  so  nearly  related  to  what 
happens  that  it  may  be  considered  as  the  actual  thing  itself.  Such 
occurrences  result  in  the  equalization  of  energy  differences,  that 
is  to  say,  the  difference  decreases  towards  zero,  and  therefore 
every  occurrence  produces  by  its  very  nature  a  decrease  in  the  cause 
of  the  occurrence,  and  so  limits  itself.  When  the  energy  difference 
is  equalized  there  is  no  longer  any  cause  for  the  occurrence  of  any 
further  process. 

It  follows  from  this  that  every  process  proceeds  more  and  more 
slowly  as  it  approaches  its  end,  and  therefore  if  we  are  dealing 
with  continuous  phenomena  the  end  itself  can  only  be  reached 
after  unlimited  time.  The  chemical  reactions  which  we  call 
homogeneous,  those  which  take  place  in  a  single  phase,  are  repre- 

290 


REACTION   VELOCITY  AND   EQUILIBRIUM  291 

sentative  of  this,  since  no  discontinuities  have  ever  been  observed 
in  them.  Our  appliances  for  testing  and  measuring  substances 
are,  however,  exceedingly  limited  in  their  sensitiveness,  and  in 
every  such  reaction  a  definite  time  can  be  observed,  after  which 
no  further  changes  can  be  observed  in  the  system.  This  time 
increases  as  our  experimental  methods  improve,  but  nevertheless 
remains  finite. 

The  assumption  which  we  have  used,  i.  e.  that  the  systems  ex- 
amined are  in  equilibrium  and  unaffected  by  changes  in  time,  may 
be  regarded  as  fundamentally  justifiable,  and  as  being  attainable 
under  proper  conditions.  Anything  which  lies  outside  of  our 
powers  of  measurement  and  observation  is  not  an  object  of  ex- 
perience. It  is  not  the  duty  of  science  to  make  any  statements 
about  such  things,  and  moreover  science  has  no  right  to  discuss 
such  objects.  We  certainly  do  not  know  whether  the  processes 
which  we  assume  to  be  continuous  remain  continuous  in  regions 
where  we  cannot  follow  them.  If  they  do  not,  our  assumption 
concerning  the  unlimited  course  of  such  processes  has  no  value. 

Processes  which  take  place  in  time  are  characterized  by  a 
velocity.  There  are  as  many  kinds  of  velocity  as  there  are  differ- 
ent kinds  of  processes  which  take  place  in  time,  and  for  chemical 
processes  we  need  to  define  chemical  velocity.  Chemical  processes 
depend  upon  the  appearance  and  disappearance  of  substances, 
and  changes  in  the  amount  of  the  substances  involved  can  be 
measured.  Chemical  velocity  is  therefore  the  ratio  of  this  change 
in  amount  to  the  time  which  elapses  during  the  change.  The 
unit  of  time  in  this  case,  as  in  science  in  general,  is  the  second,  and 
there  are  24x60x60  =  86,400  of  this  unit  in  a  mean  solar  day. 
The  unit  in  which  the  chemical  change  is  to  be  measured  requires 
some  consideration. 

Relative  and  not  absolute  amounts  of  substances  are  used  in 
this  measurement,  and  therefore  chemical  velocity,  or  reaction 
velocity,  as  it  is  called,  is  calculated  in  terms  of  the  change  in 
relative  amounts  of  the  substances  involved.  Various  substances 


292  FUNDAMENTAL  PRINCIPLES  OF  CHEMISTRY 

are  not  to  be  measured  by  weight,  but  in  terms  of  some  chemically 
comparable  unit.  The  most  convenient  unit  has  been  found  in  the 
molar  weight  (not  the  combining  weight),  and  it  is  therefore  usual 
to  use  molar  formulae  in  expressing  results.  Suppose  that  we  are 
considering  a  chemical  reaction  which  is  described  by  the  general 
equation  m1^41  +  m2^42  +  m3v43  +  .  .  .  =n1B1+n2B2  +  n3B3  +  .  .  .  The 
reaction  velocity  of  this  process  will  be  expressed  in  terms  of 
changes  in  the  relative  amounts  of  AL,  A2,  A3 .  .  .  or  Blf  B2,  B3.  .  .  . 

Various  methods  of  expression  are  possible,  but  the  most  usual 
one  is  to  define  chemical  equilibrium  in  terms  of  the  molar  con- 
centration of  the  substances  which  take  part  in  the  reaction.  By 
molar  concentration  is  to  be  understood  the  reciprocal  of  the  volume 
in  which  a  mol  of  substance  is  contained,  and  this  value  is  to  be 
found  by  dividing  the  number  of  mols  of  the  substance  in  a  given 
system  by  the  total  volume.  This  method  of  calculation  only 
leads  to  simple  relations  when  the  volume  of  the  system  remains 
constant  during  the  reaction.  In  the  majority  of  experiments 
which  have  been  made  in  this  field  this  assumption  is  realized  (at 
least  very  closely),  and  we  can  therefore  retain  this  method  of 
calculation.  It  is  of  great  advantage,  for  the  law  which  relates 
reaction  velocity  to  concentration  is  so  simple  that  the  correspond- 
ing theoretical  considerations  take  on  an  especially  simple  and 
evident  form.  It  should  be  kept  in  mind  that  the  reaction  velocity 
for  a  process  may  have  different  values  depending  on  the  sub- 
stance used  as  basis  for  the  calculation,  provided  the  molar  co- 
efficients mlt  m2,  ra3,  .  .  .  .  nlt  n2,  ns  .  .  .  in  the  general  equation 
do  not  happen  to  be  all  equal  to  unity.  But  because  of  this  very 
equation  the  values  for  the  velocity  based  upon  different  sub- 
stances will  necessarily  be  in  simple  rational  proportion,  and  this 
proportion  will  be  determined  by  the  reciprocals  of  the  molar 
coefficients. 

Reaction  velocities  based  upon  the  formation  of  substances  are 
usually  termed  positive;  those  based  upon  the  disappearance  of 
substances  are  termed  negative.  All  velocities  which  are  based 


REACTION   VELOCITY  AND   EQUILIBRIUM  293 

on  substances  appearing  on  the  same  side  of  the  reaction  equa- 
tion will  therefore  have  the  same  sign. 

184.  VARIABLE  VELOCITY.  —  We  have  now  given  definitions 
for  the  two  quantities  which  determine  a  reaction  velocity,  —  con- 
centration and  time.  We  may  next  define  reaction  velocity  in 
any  given  case  as  the  change  in  the  molar  concentration  which 
takes  place  in  one  second.  Such  a  definition  as  this  is  not  clear, 
however,  because  the  velocity  of  chemical  reaction  is  in  general 
variable.  If  the  reaction  is  investigated  at  various  stages  wholly 
different  values  for  the  velocity,  as  defined  above,  will  be  obtained. 
The  velocity  is  itself  a  function  of  the  time  or  of  the  other  variable, 
—  the  concentration,  —  which  changes  with  time. 

Furthermore  the  velocity  is  different  at  the  beginning  and  the 
end  of  the  second  during  which  the  change  is  to  be  measured, 
and  different  results  will  be  obtained  for  the  velocity  at  any  time, 
the  results  varying  with  the  duration  of  the  observation.  In  such 
cases  the  velocity  cannot  be  based  upon  a  finite  duration,  but 
must  be  calculated  for  a  time  which  is  immeasurably  short.  If 
we  call  such  a  short  time  dt,  and  call  the  change  of  concentration 
which  takes  place  in  this  time  dc  (this  must  also  be  immeasurably 
small),  the  definition  of  a  variable  velocity  is  given  by  the  expres- 

dc 

sion  — .     Small  values  of  this  kind  cannot  be  measured,  and  we 
dt 

must  therefore  fix  them  by  indirect  means.  This  can  be  done 
either  by  calculation,  in  case  we  know  velocity  as  a  function  of 
the  concentration,  or  by  experiment.  W^e  can  replace  the  im- 

dc 

measurably  small  values  in  the  expression  —  by  finite  ones  which 

dt 

can  be  observed  and  measured,  and  which  we  will  designate  with 

^^(*  (],(* 

Ac  and  A/ ;  then  the  value  of  —  approaches  the  value  of  —  as  Ac 

*— Xf  ( /  / 

/\f* 

and  A£  are  made  smaller  and  smaller.     —  may  be  determined  for 

finite  and  easily  measurable  values,  and  then  for  values  one  half 
as  large.  If  the  two  quotients  show  a  considerable  difference^ 


294  FUNDAMENTAL  PRINCIPLES  OF  CHEMISTRY 

smaller  intervals  must  be  chosen.  An  approximate  value  for  the 
velocity  has  at  any  rate  been  obtained,  and  this  can  be  improved 
in  various  ways,  which  will  not  be  described  at  this  point. 

185.  THE  LAW  OF  REACTION  VELOCITY.  —  The  convenience 
attained  by  relating  reaction  velocities  to  the  concentrations  of  the 
substances  involved  is  immediately  evident,  for  it  leads  us  to  the 
expression  of  a  very  simple  law.  Under  similar  conditions  the 
velocity  is  proportional  to  the  concentration  of  the  substances  which 
take  part  in  the  reaction.  If  only  a  single  substance  is  changing  its 
concentration  this  law,  as  stated,  is  quite  sufficient.  If  several 
substances  take  part  in  the  reaction  the  velocity  is  proportional  to 
the  concentration  of  all  of  these  substances  and  therefore  to  their 
product.  These  concentrations  may  decrease  during  the  process, 
or,  if  the  quantities  consumed  are  replaced  from  another  phase, 
they  may .  remain  practically  constant.  Differences  of  this  kind 
affect  the  detail  of  the  course  of  the  reaction,  but  do  not  affect  the 
general  character  of  the  phenomena. 

The  history  of  the  discovery  of  this  law  is  a  complicated  one 
with  chapters  lying  very  far  apart.  The  fact  that  under  otherwise 
equal  conditions  reaction  velocity  is  proportional  to  concentration 
was  expressed  by  C.  F.  Wenzel  in  the  second  half  of  the  18th 
century,  but  without  any  experimental  support.  About  the  middle 
of  the  19th  century  Wilhelmy  investigated  the  course  of  a  typical 
chemical  reaction  of  the  simplest  sort  both  experimentally  and 
theoretically,  and  in  a  completely  convincing  manner.  Cases  in 
which  several  substances  react  wrere  considered  by  Wilhelmy,  but 
these  cases  were  only  subjected  to  thorough  treatment  about  1860 
by  Harcourt  and  Esson  and  by  Guldberg  and  Waage.  Berthelot 
and  Pean  de  St.  Gilles  had  made  measurements  on  a  more  compli- 
cated case  previous  to  this  time  but  their  treatment  of  the  case  was 
not  wholly  correct. 

The  characteristic  or  normal  course  of  a  chemical  reaction  fol- 
lows the  general  law  that  reaction  velocity  is  proportional  to  the 
product  of  the  concentrations  of  all  the  substances  involved.  The 


REACTION   VELOCITY  AND   EQUILIBRIUM  295 

concentration  of  the  original  substances  always  decreases  and 
never  increases  during  the  reaction.  Under  certain  circumstances 
it  may  remain  practically  constant.  It  follows  that  the  product  on 
which  the  calculation  is  based  has  its  greatest  value  at  the  begin- 
ning of  the  reaction,  and  that  it  either  decreases  or,  at  most,  re- 
mains constant  during  the  progress  of  the  reaction.  Every  normal 
chemical  process  which  takes  place  under  constant  conditions  of 
temperature  and  pressure,  and  therefore  in  such  a  way  that  only  the 
concentrations  change,  begins  with  its  greatest  velocity,  and  the 
velocity  decreases  during  the  process,  finally  approaches  zero 
asymptotically.  Theoretically  it  requires  infinite  time  for  the 
reaction  to  reach  completion;  practically  a  limit  is  set  by  the 
limited  accuracy  of  our  methods  of  determining  small  changes. 

Deviations  from  this  typical  course  appear  when  the  conditions 
just  mentioned  are  not  satisfied.  Suppose  that  heat  is  developed 
by  the  reaction,  and  that  this  collects  in  the  system  and  results  in 
a  rise  of  temperature.  The  velocity  will  be  increased,  and  the  pro- 
cess may  take  place  in  such  a  way  that  it  begins  slowly  and  then 
increases  in  rapidity.  Finally,  however,  the  reacting  substances 
will  become  exhausted  and  the  reaction  will  proceed  more  slowly. 
The  asymptotic  end  of  all  reactions  is  therefore  a  general  rule. 
The  case  is  similar  when  a  substance  which  accelerates  the  course 
of  the  reaction  is  produced  during  the  reaction.  In  this  case  also 
the  reaction  velocity  will  first  increase,  then  decrease,  and  finally 
drop  to  an  infinitely  slow  rate. 

186.  CATALYSERS.  —  The  velocity  with  which  various  chemical 
processes  take  place  varies  in  different  cases  between  the  extreme 
limits  of  measurement.  In  other  words,  chemical  processes  are 
known  which  proceed  so  rapidly,  and  others  which  proceed  so 
slowly,  that  we  are  quite  unable  to  determine  their  duration.  Two 
wholly  different  things  must  be  kept  separate  in  this  connection. 
If  we  cause  a  chemical  process  to  take  place  between  two  sub- 
stances —  two  liquids,  for  example  —  by  bringing  them  in  contact, 
the  reaction  will  at  first  take  place  only  where  the  different  sub- 


296  FUNDAMENTAL  PRINCIPLES   OF  CHEMISTRY 

stances  come  in  contact.  The  reaction  takes  place  at  the  surface 
where  the  substance  A  is  in  contact  with  the  substance  B.  A  layer 
made  up  of  the  product  of  the  reaction  forms  between  the  two 
masses.  This  layer  must  be  removed  in  some  way  if  the  process 
is  to  continue.  Removal  takes  place  by  diffusion  and  convection. 
The  first  of  these  effects  depends  upon  the  fact  that  all  the  sub- 
stances within  a  phase  tend  to  distribute  themselves  equally  through- 
out it.  If  an  inequality  is  present  the  substances  are  set  in  motion 
automatically  to  restore  the  equality.  Such  processes  take  place 
rapidly  only  through  very  small  distances,  and  the  time  required 
becomes  large  if  the  distance  to  be  passed  over  be  only  a  few  mil- 
limetres. Convection  or  mechanical  mixing  is  of  assistance.  By 
stirring,  beating,  and  similar  movements  the  surfaces  at  which  the 
various  substances  are  in  contact  are  increased  and  moved  into 
hitherto  inactive  portions  of  the  liquid.  After  this,  diffusion  has 
only  to  take  place  through  very  short  distances.  The  mechanical 
hindrance  to  a  chemical  process  can  be  very  greatly  reduced  in 
this  way. 

These  things  are  of  great  practical  importance,  but  they  have  no 
direct  bearing  on  the  velocity  in  the  chemical  sense  of  the  term. 
In  many  cases  it  is  possible  to  complete  this  mechanical  mixing 
between  various  substances  before  an  appreciable,  or  at  any  rate 
considerable,  fraction  has  reacted  chemically,  and  from  this  point 
on  the  true  reaction  velocity  shows  itself.  The  chemical  process 
takes  place  slowly  in  the  homogeneous  solution,  and  may  be  fol- 
lowed by  measurement  of  the  corresponding  change  in  its  proper- 
ties. Slow  and  rapid  processes  may  be  differentiated  now  without 
difficulty;  some  of  them  are  so  rapid  that  the  reaction  is  complete 
as  soon  as  mixture  is  complete.  In  this  case  it  is  only  the  end 
products  which  are  open  to  investigation.  Other  reactions  are  so 
slow  that  the  properties  of  the  unchanged  original  solution  can  be 
determined  at  leisure  before  the  chemical  process  has  exerted  any 
appreciable  influence  upon  them.  We  must  of  course  assume  that, 
theoretically,  a  portion  of  the  substances  involved  has  been  trans- 


REACTION   VELOCITY  AND   EQUILIBRIUM  297 


formed  in  this  case  as  well  as  in  others,  and  all  that  we  can  state 
is  that  this  portion  is,  under  some  circumstances,  quite  inappreci- 
able. This  can  be  proven  by  repeating  the  measurements  after 
an  interval  to  see  whether  the  same  result  is  obtained. 

The  factors  which  determine  the  velocity  in  any  given  case  are 
still  to  a  large  extent  unknown  to  us.  Temperature  has  a  very 
great  effect  on  reaction  velocity,  the  latter  increasing  rapidly 
with  rising  temperature.  Chemical  reaction  velocity  is  the  most 
variable  of  all  the  things  which  vary  with  temperature;  in  round 
numbers  it  doubles  for  a  temperature  increase  of  10°.*  One  of  the 
properties  which  varies  most  rapidly  with  temperature  is  the  viscos- 
ity of  liquids  and  this  changes  by  about  2  per  cent  per  degree, 
doubling  its  value  for  a  temperature  change  of  about  50°.  The 
increase  in  reaction  velocity  is  an  exponential  function  of  the 
temperature.  An  increase  of  10°  in  temperature  doubles  it;  for 
20°  it  is  multiplied  by  4,  for  30°  by  8,  etc.  It  will  be  seen  from 
this  that  a  rise  in  temperature  of  100°,  a  very  moderate  one 
practically,  corresponds  to  an  increase  of  a  thousandfold  in 
reaction  velocity. 

Reaction  velocity  shows  a  similar  sensitiveness  to  other  effects. 
A  change  of  solvent  in  which  given  substances  react  under  other- 
wise constant  conditions  of  concentration  and  temperature  may 
produce  a  change  in  velocity  within  the  most  extreme  limits.  The 
same  substances  may  react  stormily  or  appear  practically  indiffer- 
ent to  each  other,  so  that  no  apparent  change  takes  place  after  hours 
and  days,  and  this  variation  may  be  produced  by  changing  the 
medium  in  which  they  are  dissolved.  Nothing  very  definite  is 
known  of  this  effect,  but  it  may  be  stated  broadly  that  those  sol- 
vents which  contain  oxygen  usually  exhibit  more  rapid  reactions 
than  those  which  are  free  from  oxygen. 

There  are  also  a  large  number  of  substances  which  affect  the 
velocity  of  a  given  reaction  even  when  they  are  present  only  in 

*  The  change  in  vapour  pressure  of  a  liquid  is  a  function  of  the  temperature 
of  about  the  same  order. 


298  FUNDAMENTAL  PRINCIPLES  OF  CHEMISTRY 

very  small  amount.  In  the  majority  of  cases  these  substances  do 
not  take  part  in  the  chemical  process,  or  at  least  they  are  found 
practically  unchanged  in  amount  in  the  reacting  mixture  before, 
during,  and  after  the  reaction.  It  does  not  necessarily  follow 
from  this  that  they  take  no  part  in  the  reaction.  We  need  only 
to  assume  that  their  activity  is  a  transient  one,  and  that  they  are 
formed  in  unchanged  amount  from  the  products  of  reaction  in 
case  they  do  react  with  any  of  the  substances  present.  They 
may,  for  example,  be  constituents  of  intermediate  products  of  the 
reaction,  and  as  the  process  goes  on  these  intermediate  products 
are  broken  up,  setting  the  original  substance  free. 

Such  substances  are  called  catalysers,  and  they  show  the  same 
remarkable  versatility  in  their  quantitative  effects  as  has  been 
already  observed  in  reaction  velocities  in  general.  The  very 
smallest  amounts  of  substance  sometimes  show  very  considerable 
effects,  and  of  all  our  methods  of  detecting  very  small  amounts 
those  which  depend  upon  catalytic  action  are  by  far  the  most 
sensitive.  Sometimes  our  ordinary  means  of  detecting  a  definite 
substance  fail  completely,  and  a. given  object  may  appear  to  be 
completely  free  from  that  substance.  In  these  conditions  it  is 
sometimes  possible  to  prove  the  actual  presence  of  the  substance 
by  measuring  the  catalytic  effect  of  the  other  substance  in  which  it 
is  supposed  to  be  contained.  The  greatest  dilution  in  which  a 
particular  element  has  been  determined  in  this  way  is  about  one 
mol  in  a  billion  litres. 

A  catalytic  effect  is,  in  the  majority  of  cases,  an  acceleration  of 
a  reaction,  that  is,  an  increase  in  reaction  velocity.  It  is  not  yet 
completely  decided  whether  or  not  there  are  any  negative  catalysers, 
or  whether  the  actually  observed  decrease  in  reaction  velocity  is 
a  secondary  effect  due  to  small  amounts  of  foreign  substances. 
These  would  act  by  destroying  the  effect  of  accelerating  catalysers 
which  might  be  present.  However  this  may  be,  negative  catalysers 
are  comparatively  much  rarer  than  positive  ones,  of  which  there 
are  a  very  great  number. 


REACTION   VELOCITY  AND   EQUILIBRIUM  299 

Catalysers  are  all  more  or  less  specific  in  their  action,  and  each 
special  reaction  shows  its  own  individual  peculiarity  with  respect 
to  foreign  substances  which  affect  its  velocity.  There  are,  to  be 
sure,  some  substances  which  catalyse  many  different  reactions, 
but  their  effect  cannot  be  reduced  to  two  factors,  one  of  which 
depends  only  on  the  catalyser  and  the  other  on  the  reaction.  In- 
fluences are  active  which  differ  from  case  to  case,  and  no  relation 
with  other  properties  or  factors  has  as  yet  been  recognised. 

The  predominance  of  positive  catalysers  is  connected  with  the 
fact  that  very  pure  substances  often  react  extremely  slowly  with 
each  other.  The  active  amounts  of  catalytic  substances  are  often 
very  much  smaller  than  anything  we  can  detect  by  other  means. 
It  would  therefore  be  impossible  to  refute  the  statement  that  pure 
substances  do  not  react  at  all  with  appreciable  velocity,  and  that 
all  our  actual  reactions  are  caused  by  the  presence  of  extremely 
small  amounts  of  catalytically  active,  foreign  substances.  If  this 
statement  cannot  be  refuted  it  is  also,  and  for  the  same  reasons, 
impossible  of  proof.  It  can,  however,  in  general  be  concluded 
that  an  unknown  catalyser  is  active  whenever  the  velocity  of  a 
certain  reaction  is  found  to  vary  under  apparently  constant  con- 
ditions, the  concentration  or  some  other  peculiarity  of  the  catalyser 
constituting  a  variable  among  conditions  which  we  are  assuming 
constant. 

187.  IDEAL  CATALYSERS.  —  The  existence  of  catalysers  is  of 
importance  in  the  general  theory  of  chemistry,  for  they  enable  us 
to  carry  out  idealized  simplifications  of  actual  processes.  Every 
science  makes  use  of  these  idealizations.  In  mechanics,  for  ex- 
ample, absolutely  stiff  bodies,  absolutely  mobile  liquids,  etc.,  play 
an  important  part.  In  other  divisions  of  physics  we  use  absolutely 
perfect  gases,  which  obey  the  gas  equation  exactly,  absolutely  per- 
fect insulators  for  heat  and  electricity,  absolutely  black  bodies, 
perfectly  reflecting  mirrors,  etc.  None  of  these  things  exist  as  a 
matter  of  fact,  and  their  assumption  constitutes  a  conscious  devia- 
tion from  the  true  conditions.  They  are,  however,  limiting  cases 


300  FUNDAMENTAL   PRINCIPLES  OF   CHEMISTRY 

toward  which  actual  things  approximate  more  or  less  perfectly, 
and  they  also  permit  of  simple  numerical  treatment  because  of 
the  simplicity  in  the  assumptions  made  in  treating  them.  Results 
of  calculations  based  on  them  are  therefore  never  absolutely  cor- 
rect, but  these  ideal  cases  have  been  so  chosen  that  the  result 
approaches  accuracy  in  the  same  measure  that  the  actual  con- 
ditions approach  those  assumed.  This  permits  of  a  corresponding 
predetermination  of  actual  conditions.  A  further  advantage  is 
afforded  by  these  limiting  cases.  They  teach  us  the  aspect  of 
actual  phenomena  which  are  best  suited  to  lead  us  toward  the  ideal 
limiting  case.  For  example,  the  formula  for  the  ideal  pendulum 
indicates  immediately  the  best  way  to  construct  an  actual  pendu- 
lum which  will  possess  the  most  important  property  of  the  ideal 
one,  —  equal  time  of  swing. 

In  this  sense  catalysers  afford  a  theoretical  means  of  producing 
ideal  chemical  conditions.  Suppose  that  we  are  examining  a  sys- 
tem in  which  a  reaction  is  taking  place  very  slowly  indeed.  If  we 
add  an  exceedingly  active  accelerator  the  system  becomes  free  from 
changes  in  time,  that  is,  it  enters  a  state  of  equilibrium.  All  the 
investigations  which  we  have  carried  out  up  to  now  can  be  con- 
sidered as  having  been  carried  out  in  this  ideal  way.  All  these 
chemical  processes  might  have  taken  place  under  the  influence  of 
such  an  ideal  accelerator,  for  we  have  invariably  started  with  the 
assumption  that  complete  equilibrium  existed.  Or,  on  the  other 
hand,  we  might  assume  ideal  negative  catalysers,  or  the  equivalent 
assumption  that  no  reaction  takes  place  without  an  accelerator 
and  that  no  accelerator  is  present.  Every  system  in  process  of 
chemical  change  could  then  be  fixed  firmly  in  its  condition,  and  the 
substances  present  considered  as  exerting  no  further  effect  on  each 
other.  None  of  these  things  can  be  carried  out  actually,  and  this 
is  in  agreement  with  the  physical  ideals  considered  above.  Our 
method  shares  with  them  the  advantage  that  it  permits  of  far- 
reaching  simplification  and  of  arriving  at  conclusions  which  ap- 
proximate the  actual  facts  more  or  less  closely. 


REACTION   VELOCITY  AND   EQUILIBRIUM  301 

In  making  use  of  any  such  idealization  the  question  must  always 
be  raised  whether  the  assumptions  do  not  conflict  with  any  actual 
relations,  for,  if  they  do,  conclusions  drawn  will  no  longer  be  limit- 
ing values  but  false  ones.  It  is,  in  general,  impossible  to  answer 
such  a  question  exhaustively,  but  it  is  possible  to  show  a  contra- 
diction with  the  most  general  of  all  laws,  the  laws  of  energy,  if  any 
such  contradiction  exists.  In  the  case  of  the  ideal  catalysers  it 
does  not  exist.  The  assumption  of  these  accelerators  presupposes 
that  the  velocity  of  a  chemical  process  may  have  any  value  between 
zero  and  infinity  without  a  proportional  variation  in  the  energy 
involved.  It  is  a  physical  fact  that  catalysers  do  exist  which  permit 
of  variations  in  reaction  velocity  between  very  wide  finite  limits, 
though  not,  of  course,  between  infinite  limits.  With  their  aid  it 
has  been  proven  that  very  large  finite  variations  in  reaction  velocity 
can  be  brought  about  without  expenditure  of  energy,  and  the 
transition  to  ideal  catalysers  is  therefore  justified.  As  far  as  energy 
is  concerned,  only  the  final  condition  of  a  system  is  determined 
when  the  conditions  affecting  it  are  stated.  Nothing  need  be  given 
about  the  time  within  which  this  final  condition  is  to  be  reached. 
As  among  mechanical,  electrical,  thermal,  and  other  systems,  other 
factors  are  effective  in  chemical  systems  also,  and  these  factors 
are  not  definitely  determined  by  the  two  laws  of  energetics.  A 
corresponding  freedom  remains  in  the  matter  of  reaction  velocity. 

Reaction  velocities  can  vary  from  zero  to  infinity,  and  this  corre- 
sponds to  a  degree  of  complexity  among  chemical  systems  far 
greater  than  any  which  could  be  foreseen  from  our  previous  dis- 
cussion. Systems  which  are  by  no  means  in  equilibrium,  but  in 
which  the  reaction  velocity  is  infinitesimal,  appear  to  us  as  systems 
in  equilibrium.  It  means  also  that  substances  and  solutions  which 
would  have  been  for  ever  unknown  to  us,  if  all  earthly  chemical 
processes  took  place  within  unlimitedly  high  velocities,  are  open  to 
our  observation  and  demand  our  consideration.  New  problems, 
especially  those  of  isomerism  and  constitution,  are  presented  to  us 
as  a  result,  and  they  will  be  taken  up  later. 


302  FUNDAMENTAL  PRINCIPLES  OF  CHEMISTRY 

188.  CHEMICAL  EQUILIBRIA.  —  Suppose  we  have  a  reaction 
equation  of  the  form  mlA1+m2A2  +  m3A3  +  .  .  .=n1B1+n2B2  + 
n3B3  +  .  .  .,  the  substances  at  the  left  being  transformed  into  those 
at  the  right.  It  is  often  possible  to  find  conditions  of  temperature 
and  pressure  such  that  the  reaction  takes  place  in  the  opposite 
direction,  the  substances  at  the  right  disappearing  and  those  at 
the  left  being  formed.  It  will  be  remembered  that  it  requires  an 
unlimited  number  of  operations  to  separate  the  two  constituents 
of  a  solution  completely.  The  converse  of  this  would  be  that  the 
first  traces  of  substances  would  appear  with  unlimited  intensity  in 
systems  where  these  substances  do  not  exist,  but  in  which  they  can 
be  produced  from  other  substances  which  are  present.  As  a  matter 
of  fact  we  would  be  very  nearly  in  agreement  with  observed  facts 
if  we  should  assume  that  all  the  substances  which  are  possible 
under  given  conditions  are  really  present,  though  they  are  often 
present  in  concentrations  lying  more  or  less  below  the  limit  of 
detection. 

There  is  good  reason  for  this  assumption,  for,  as  our  analytical 
methods  advance,  more  and  more  processes  are  found  which  are 
actually  limited  by  an  opposing  process  in  just  the  way  that  has 
been  mentioned  above.  The  number  of  processes  which  belong 
to  this  class  is  being  constantly  increased  by  these  discoveries, 
and  processes  once  placed  in  this  class  always  remain  there.  It 
follows  that  the  class  must  always  increase  and  never  decrease. 
No  characteristic  has  ever  been  discovered  which  differentiates 
these  balanced  reactions  from  the  others,  which  we  are  obliged 
to  consider  as  one-sided  for  lack  of  proof  that  the  opposed  reaction 
takes  place.  We  are  in  agreement  with  the  general  inductive 
methods  of  science  if  we  assume  that  all  reactions  belong  in  the 
class  of  balanced  ones,  at  least  until  proof  is  given  that  this  is  not 
true. 

This  conclusion  is  limited  by  the  assumptions  involved  in  it. 
Our  reasoning  is  based  upon  a  general  property  of  solutions,  and 
its  application  must  therefore  be  limited  to  solutions.  If  there- 


REACTION  VELOCITY  AND   EQUILIBRIUM  303 

fore  a  chemical  reaction  takes  place  among  solids  which  are  not 
mutually  soluble  in  appreciable  amount,  it  is  not  necessary  to 
assume  a  chemical  equilibrium  in  which  all  possible  substances 
are  actually  represented.  It  may  still  be  doubted  whether  this 
new  assumption  of  mutual  insolubility  is  fulfilled  even  among 
solids,  and  it  seems  possible  that  our  general  reasoning  may  be 
applicable  to  them  also;  but  if  the  limit  of  solubility  is  beyond 
experimental  investigation  it  has  no  practical  interest,  and  these 
cases  may  be  treated  as  though  the  substances  involved  were  per- 
fectly insoluble  in  each  other.  This  conclusion,  which  was  reached 
experimentally,  is  in  no  way  different  from  the  one  which  might 
be  drawn  from  the  assumption  that  the  solubility  among  solids 
is  finite  but  small  beyond  the  limits  of  measurement. 

Under  the  given  conditions  each  reaction  will,  in  general,  take 
place  in  both  directions,  but  the  final  result  of  the  reaction  will 
depend  upon  the  velocity  of  each  of  the  two  opposed  reactions. 
The  observed  change  will  be  made  up  of  the  difference  of  the  two 
opposed  reactions.  Let  us  suppose  to  begin  with  that  one  of  the 
two  processes  predominates,  and  that  this  is  the  direct  one.  The 
concentration  of  the  substances  which  are  in  transformation  will 
be  constantly  decreased  by  the  reaction,  and  the  concentration  of 
the  products,  that  is  to  say,  of  the  substances  which  produce  the 
opposed  reaction,  will  increase  simultaneously.  Both  causes  will 
act  in  slowing  down  the  direct  action  and  in  accelerating  the  op- 
posed one,  and  this  will  continue  until  both  processes  are  taking 
place  with  the  same  velocity.  From. this  point  on  there  will  be 
formed  in  unit  time  an  amount  of  the  products  of  the  direct  re- 
action equal  to  the  amount  used  up,  and  the  condition  of  the  system 
will  no  longer  change  with  time.  This  is  the  definition  of  a  chemical 
equilibrium,  and  it  is  characterized  as  such  in  a  system  containing 
several  substances  in  one  homogeneous  phase  by  the  fact  that  all 
possible  substances  are  present  in  definite  concentrations  which 
vary  with  pressure,  temperature,  and  the  nature  of  the  substances 
involved. 


304  FUNDAMENTAL   PRINCIPLES  OF   CHEMISTRY 

It  happens  very  often  that  these  concentrations  are  immeasur- 
ably small  for  substances  which  lie  on  one  side  of  the  reaction 
equation,  and  in  this  case  the  reaction  is  practically  unidirectional. 
Such  cases  have  always  been  of  special  interest  in  experimental 
and  technical  chemistry,  since  they  permit  of  the  preparation  of 
pure  substances  with  the  greatest  ease,  and  pure  substances  are, 
and  always  have  been,  of  great  interest  both  in  science  and  in 
technical  affairs.  The  idea  that  such  unidirectional  processes 
were  normal  or  typical  ones,  while  chemical  equilibrium  with  its 
finite  concentrations  of  the  substances  involved  was  an  exception, 
has  been  handed  down  to  us  from  earlier  times.  As  our  knowledge 
of  chemical  reactions  became  more  complete  and  extended  it  was 
found  that  these  finite  equilibria  were  not  by  any  means  rare,  and 
they  are  of  much  greater  theoretical  interest  at  the  present  time 
than  other  reactions. 

189.  MORE  THAN  ONE  PHASE.  —  The  appearance  of  a  new 
phase  beside  the  original  one  produces  a  very  great  effect  upon  the 
equilibrium  of  a  given  chemical  system.  As  we  have  already 
seen,  the  concentration  of  the  individual  substances  existing  side 
by  side  in  several  phases  affect  each  other  mutually,  and  the  result 
is  a  condition  of  "  saturation."  If  we  have  a  gas  in  contact  with 
a  liquid  its  concentration  in  the  liquid  can  never  be  greater  than 
that  given  by  Henry's  Law  (Sec.  98).  If  the  gaseous  substance  in 
question  is  produced  in  the  liquid  phase  until  the  solution  contains 
a  larger  amount  than  is  permissible  by  Henry's  Law,  the  excess 
escapes  in  the  form  of  gas.  As  this  takes  place  further  amounts 
of  the  same  substance  are  produced,  and  the  equilibrium  in  the 
liquid  phase  is  shifted  more  and  more  in  the  sense  which  permits 
of  the  formation  of  more  gas.  Finally,  saturation  equilibrium  with 
the  gas  phase  is  attained  in  addition  to  any  other  chemical  equi- 
librium which  may  exist  in  the  liquid.  If  the  saturation  equilibrium 
corresponds  to  a  very  small  amount  of  dissolved  gas,  because  of 
low  pressure  and  slight  solubility,  then  the  reaction  within  the 
liquid  will  go  on  until  equilibrium  is  reached  as  the  result  of  this 


REACTION   VELOCITY  AND   EQUILIBRIUM  305 

small  concentration.  This  means  that  the  reaction  by  which  the 
gas  is  formed  will  be  greatly  predominant  over  the  opposed 
reaction,  and  it  may  often  appear  to  be  a  practically  com- 
plete one. 

This  peculiarity  among  chemical  equilibria  was  noticed  more 
than  a  century  ago  by  C.  L.  Berthollet.  He  recognised  that  the 
tendency  of  a  substance  to  take  on  gaseous  form  (he  called  it  "  elas- 
ticity") was  a  circumstance  which  favoured  the  almost  exclusive 
formation  of  this  particular  substance  by  chemical  reactions  in 
which  it  could  appear. 

Similar  conditions  are  applicable  when  one  of  the  substances 
in  question  possesses  the  property  of  separating  as  a  solid  phase 
of  slight  solubility.  Here  again  the  greatest  concentration  which 
this  substance  can  have  in  the  liquid  is  given  by  the  concentration 
of  its  saturated  solution,  and  the  equilibrium  will  therefore  shift 
as  the  solid  phase  separates  until  the  concentration  of  saturation 
in  the  solution  is  sufficient  to  maintain  equilibrium  against  the 
concentration  of  the  other  substances.  The  formation  of  such 
a  difficultly  soluble  solid  will,  under  these  circumstances,  take 
place  so  easily  that  the  reaction  will  often  appear  to  take  place 
exclusively  for  the  benefit  of  its  formation. 

Berthollet  understood  this  case  also  and  called  it  the  effect  of 
"  cohesion." 

We  have  developed  this  case  for  the  liquid  phase  made  up  of 
a  solution  of  the  substances  taking  part,  and  a  precisely  similar 
conclusion  may  be  drawn  for  the  case  where  the  solution  phase 
is  gaseous.  The  great  rarity  of  solid  solutions  practically  excludes 
the  third  probability. 

190.  THE  LAW  OF  MASS  ACTION.  —  Our  conclusions  concerning 
the  setting  up  of  a  chemical  equilibrium  by  the  equalization  of  op- 
posed reaction  velocities  leads  directly  to  a  mathematical  expression 
in  which  the  equilibrium  is  expressed  as  a  function  of  the  concen- 
trations of  the  substances  which  take  part.  It  is  only  necessary 
to  set  down  the  velocities  of  the  two  opposed  reactions  as  being 
20 


306  FUNDAMENTAL  PRINCIPLES  OF  CHEMISTRY 

equal.  If  m^Av  +  m2A2  +  m3A3  +..-•=  nlBl  +  n2B2  +  n3B3  +  • . . 
and  a1}  a2,  a3  and  blt  b2}  bs  are  the  concentrations  of  the  substances 
on  the  two  sides  of  the  reaction  equation,  then  the  velocity  of  the 
first  reaction  is  given  by  the  expression  (^  =  &1o1miaa"l»aiw»  ••  •, 
and  that  of  the  second  by  c2  =  k^b^b^bs713  •  •  • .  The  two  velocities 
are  to  be  equal,  and  therefore  klajn*ajn*ajn*  -•  •  =  kjb^b.pbj1*  -  •  • , 
or  writing  ^_  a^a^a^^ 

&i        '  b^b^bsn,..-    ' 

Expressed  in  words,  equilibrium  exists  if  the  product  of  the  con- 
centrations on  one  side  of  the  reaction,  divided  by  the  correspond- 
ing product  for  the  other  side,  is  a  constant.  It  should  be  noticed 
that  this  constant  is  only  to  be  considered  as  constant  with  respect 
to  differences  of  concentration.  Its  value  still  depends  upon  the 
temperature. 

The  special  cases  mentioned  in  the  previous  paragraph  follow 
directly  from  this  formula.    Let  us  consider  the  simplest  case,  - 
in  which  only  one  substance  is  present.     The  reaction  will  be 

mA=nB,  and  the  equation  for  equilibrium  will  be  r^-  =  K.     If 

the  concentration  b  is  reduced  in  any  way  4^y  the  formation  of  a 
gas  or  of  a  difficultly  soluble  solid,  for  example,  then  a  must  also 
decrease  in  the  same  proportion  if  K  is  to  remain  constant.  This 
means  that  a  corresponding  amount  of  A  will  change  into  B  before 
equilibrium  can  exist.  As  far  as  the  formation  of  B  is  concerned 
the  reaction  is  practically  complete. 

Similar  conclusions  apply  when  several  substances  occur  on  one 
or  both  sides  of  the  equation.  If  one  factor  of  the  product  is  very 
small  the  entire  product  must  be  small,  for  it  is  not  usually  possi- 
ble that  another  factor  should  be  very  large  at  the  same  time. 
The  concentrations  of  substances  have  finite  limits  because  of 
their  finite  specific  volumes,  and  it  is  only  possible  to  compensate 
for  the  small  value  of  one  factor  by  an  increase  in  another  within 
a  very  narrow  range. 


REACTION   VELOCITY   AND   EQUILIBRIUM  307 

191.  EXPLANATION  OF  ANOMALOUS  CASES.  — Science  is  forced 
to  the  assumption  of  chemical  equilibrium  between  opposed  re- 
actions in  another  way.  The  assumption  is  necessary  for  the  ex- 
planation of  certain  contradictions  between  general  laws  which 
are  characteristic  of  the  properties  of  pure  substances.  Gases 
are  known  which  appear  hylotropic  throughout  a  large  range  of 
pressures  and  temperatures.  Judged  by  this  criterion  they  act 
like  pure  substances,  but  these  gases  by  no  means  obey  the  general 
laws  of  gases.  They  do  not  exhibit  the  normal  coefficient  of  ex- 
pansion', their  volume  is  not  inversely  proportional  to  the  pressure, 
and  they  do  not  follow  the  volume  law  of  Gay-Lussac.  These 
contradictions  are  removed,  and  these  gases  can  be  arranged  under 
general  laws,  if  we  assume  that  they  are  mutual  solutions  of  two 
or, more  substances  which  can  react  with  one  another  chemically. 
But  we  have  said  that  solutions  of  gases  behave  like  pure  sub- 
stances as  far  as  obedience  to  the  general  equation  is  concerned, 
and  the  assumption  just  made  cannot  therefore  explain  these 
deviations.  If  we  make  the  further  assumption  that  the  ratio  of 
the  constituents  in  the  solution  changes  with  temperature  and 
pressure,  it  is  possible  to  explain  the  anomalies  in  question,  pro- 
vided the  volume  changes  during  reaction.  Suppose  a  reaction 
of  the  form  A2  =  2A,  A  being  either  an  element*  or  a  compound. 
A  solution  of  these  substances  A  and  A2  would  behave  in  the  man- 
ner just  described,  provided  the  proportion  of  the  two  constituents 
changed  with  pressure  and  temperature.  If  a  decrease  of  pressure 
causes  A2  to  change  into  A  the  gas  will  behave  normally  under 
very  small  or  very  large  pressures,  for  in  the  first  case  it  will  con- 
tain almost  wholly  A  and  in  the  second  almost  wholly  A2,  in  either 
case  with  only  a  minute  amount  of  the  other  substance.  Consider- 
able changes  of  temperature  must  produce  the  same  effect  if  the 
equilibrium  is  variable  with  temperature.  These  peculiarities 
correspond  very  closely  with  those  actually  observed.  All  of  these 
irregular  gases  become  normal  at  high  temperatures  and  low  pres- 
sures, and  under  these  conditions  they  obey  Gay-Lussac's  Law. 


308  FUNDAMENTAL   PRINCIPLES  OF  CHEMISTRY 

This  idea  has  also  other  applications.  Let  us  apply  the  law  of 
mass  action,  as  given  in  Sec.  190,  to  these  chemical  equilibria, 
and  especially  to  their  dependence  upon  pressure,  which  is,  in 
this  case,  proportional  to  concentration.  With  the  aid  of  this  law 
it  is  possible  to  represent  quantitatively,  not  only  the  limiting  con- 
ditions, but  also  all  the  intermediate  states  of  this  system.  Sup- 
pose we  have  1  mol  of  the  substance  A2,  and  we  will  assume  that 
a  fraction  x  of  this  mol  has  been  transformed  into  A.  The  state 
of  the  gas  solution  can  now  be  determined  by  the  statement  that 
its  r  value  must  be  made  up  of  the  sum  of  the  corresponding  partial 
values  of  the  constituents  A  and  A2.  2x  mols  of  A  are  present  and 
l-x  mols  of  B.  We  have  therefore  r=(l-x)R+2xR  =  (l+x)R 
and  the  equation  pv—(l+x)RT  will  hold  for  the  solution.  If 
#  =  0,  pv  =  RT;  if  x  =  l,  pv  =  2RT,  and  these  are  the  two  limiting 
cases.  If  p,  v,  and  T  are  measured  for  an  amount  of  gas  correspond- 
ing to  1  mol  of  A2,  x  can  be  determined  for  any  given  condition. 

From  r  =  (I  +  x)R  we  obtain  x  =  — — — .    r  has  been  measured  and 

R 

R  has  a  constant  value  (see  Sec.  174),  and  the  value  of  x  is  thus 
determined. 

Applying  the  law  of  mass  action  to  this  case  we  obtain  the 

equilibrium  equation  ^|  =  K  from  the  reaction  equation  A2  =  2A. 

The  concentrations  a  and  a2  are   proportional  to  their   amounts 
2x  and  1  —  x,  since  the  two  gases  form  a  solution  and  therefore 

n  —x}2 
both  occupy  an  equal  volume.     It  follows  that    ^-75 — -  =  K,     K 

2i3C 

being  a  constant,  and  from  this  that  the  concentration  of  A  must 
change  in  the  proportion  of  the  inverse  square  of  the  concentration 
of  A  2  under  the  influence  of  a  change  of  pressure,  provided  the  law 
of  mass  action  holds.    Experiment  has  confirmed  this  deduction. 
192.   THE   QUANTITATIVE   INVESTIGATION   OF   EQUILIBRIA.  - 
What  facts  lead  us  to  assume  a  condition  of  chemical  equilibrium 
in  a  liquid  phase  ?    Let  us  assume  the  most  general  case.    Two  or 


REACTION   VELOCITY  AND   EQUILIBRIUM  309 

more  substances  are  brought  together  which  can  not  only  form  a 
solution,  but  which  can  also  react  chemically  to  form  new  sub- 
stances, which  in  turn  form  solutions  with  each  other  and  with  the 
unchanged  residue.  What  phenomena  force  us  to  the  assumption 
that  a  reaction  has  taken  place  and  that  new  substances  have  been 
formed  ?  It  has  been  already  shown  by  general  reasoning  that 
when  no  new  phase  separates  it  is  theoretically  impossible  to  dis- 
criminate in  the  case  of  liquids  between  a  solution  and  a  chemical 
reaction.  If,  however,  we  caused  separation  and  removed  a  phase 
by  distillation  we  found  that  the  most  volatile  substance  would  be 
the  first  to  separate.  The  chemical  equilibrium  will,  under  these 
circumstances,  be  shifted  in  such  a  way  that  this  particular  sub- 
stance will  be  formed.  These  new  amounts  will  continue  to  distil 
over,  and  we  will  finally  obtain  not  only  an  amount  of  this  substance 
equal  to  the  amount  originally  present,  but  as  much  as  could  pos- 
sibly be  produced  from  the  substances  in  the  system.  The  other 
constituents  remain  in  the  residue.  The  substance  so  removed  by 
distillation  may  either  be  one  of  the  original  substances  or  a  prod- 
uct of  the  reaction.  In  the  first  case  we  must  conclude  that  no 
chemical  process  has  taken  place;  in  the  second,  that  a  complete 
reaction  has  been  carried  out.  In  neither  case  could  we  conclude 
anything  about  an  equilibrium  involving  the  presence  of  all  possible 
substances. 

This  is  in  fact  the  condition  of  things  in  many  cases  where  the 
assumption  of  chemical  equilibrium  in  the  presence  of  all  possible 
substances  depends  upon  more  or  less  indirect  conclusions.  This 
is  the  case  when  the  velocity  with  which  equilibrium  (as  measured 
by  the  concentrations  in  the  system)  is  restored  after  being  dis- 
turbed, is  very  great  in  proportion  to  the  velocity  with  which  the 
distillation  or  other  operation  is  carried  out.  Equilibrium  either 
continues  unchanged  during  such  an  operation  or  else  it  is  attained 
immediately  after  the  separation  of  one  or  the  other  of  the  con- 
stituents. It  is  never  possible  to  isolate  a  group  of  substances 
which  belongs  on  one  side  or  the  other  of  the  reaction  equation. 


310  FUNDAMENTAL  PRINCIPLES   OF  CHEMISTRY 

This  condition  of  things  is  reversed  when  the  velocity  relation  is 
of  the  opposite  sort.  If  separation  can  be  carried  out  by  causing 
new  phases  to  form  before  the  new  equilibrium  is  attained  as  a 
result  of  a  change  in  concentration,  then  the  system  behaves  as 
though  no  mutual  reaction  whatever  took  place  between  the  sub- 
stances. The  ordinary  operations  of  separation  yield  the  substances 
which  take  part  in  the  equilibrium  in  approximately  the  same  pro- 
portions as  those  in  which  they  were  originally  present.  In  this 
way  it  is  possible  to  show  whether  or  not  a  chemical  reaction  has 
taken  place,  and  in  the  latter  case  it  is  possible  to  determine  the 
proportions  corresponding  to  equilibrium. 

The  assumption  of  ideal  catalysers  (see  Sec.  187)  enables  us 
to  set  up  ideal  conditions.  We  will  first  add  to  the  system  a 
catalyser  which  results  in  producing  equilibrium  instantly.  Then 
we  will  suppose  this  catalyser  to  be  removed,  or,  still  better,  re- 
placed by  an  absolutely  negative  catalyser.  Analysis  can  then  be 
carried  out  at  leisure,  since  no  further  change  can  take  place  under 
our  assumptions. 

It  is  possible  to  approximate  this  ideal  condition  of  things 
when  a  gas  reaction  is  under  investigation  at  high  temperatures. 
Under  these  conditions  (see  Sec.  186)  equilibrium  is  very  rapidly 
reached.  If  the  gas  is  now  suddenly  cooled  by  leading  it  from  the 
vessel  in  which  the  reaction  has  taken  place  through  a  narrow, 
well-cooled  tube,  it  will  remain  fixed  in  its  condition,  since  the 
reaction  velocity  at  the  low  temperature  is  practically  zero.  The 
nature  of  the  gases  in  question  can  then  be  determined  by  ordinary 
analytical  methods.  In  liquid  systems  it  is  also  sometimes  pos- 
sible to  greatly  retard  a  reaction  by  suddenly  cooling  the  liquid, 
and  in  this  case  also  an  approximate  analysis  can  be  carried  out. 

193.  Is  EQUILIBRIUM  AFFECTED  BY  A  CATALYSER  ?  —  The 
method  just  described  only  leads  to  correct  results  if  the  chemical 
equilibrium  is  not  shifted  by  the  addition  of  the  catalyser.  The 
latter  has  a  great  effect  on  the  reaction  velocity,  and  it  has  been 
shown  that  equilibrium  is  determined  by  the  ratio  of  the  opposed 


REACTION   VELOCITY  AND   EQUILIBRIUM  311 

reaction  velocities.  It  might  therefore  be  supposed  that  a  catalyser 
would  have  a  decided  influence  on  equilibrium.  As  a  matter  of 
fact  our  assumptions  are  correct,  and  a  catalyser  cannot  affect 
equilibrium  in  spite  of  the  fact  that  it  may  have  so  great  an  influence 
on  the  reaction  velocity. 

This  conclusion  may  be  drawn  from  general  reasoning.  A 
chemical  equilibrium  cannot  be  changed  without  the  expenditure 
of  a  corresponding  amount  of  work,  for  equilibrium  is  that  condi- 
tion in  which  the  system  has  already  given  up  the  whole  of  its  avail- 
able energy.  If  any  work  is  still  available  a  corresponding  change 
in  the  system  would  take  place  of  its  own  accord,  that  is,  the  system 
is  not  in  equilibrium.  On  the  other  hand,  if  the  condition  of  a 
system  in  equilibrium  is  to  be  changed,  work  must  be  furnished 
from  without.  Addition  of  the  catalyser  does  not  correspond  to 
furnishing  work,  for,  by  our  definition,  the  catalyser  is  in  the  same 
condition  at  the  end  of  the  reaction  as  at  the  beginning,  and  it 
can  therefore  have  furnished  no  work.  A  shift  of  equilibrium,  due 
to  the  catalyser,  would  therefore  be  in  contradiction  to  the  second 
law,  and  it  is  a  matter  of  experience  that  we  know  of  no  such 
contradiction. 

These  two  .effects,  influence  on  reaction  velocity  and  lack  of 
influence  on  equilibrium,  are  the  basis  for  the  conclusion  that  a 
catalyser  which  influences  a  reaction  must  also  influence  the  op- 
posed reaction  in  the  same  sense  and  in  the  same  proportion.  If 
it  accelerates  the  direct  process  it  must  accelerate  the  reverse  one 
in  the  same  way.  Only  when  this  is  true  can  the  ratio  of  the  two 
velocities  remain  unchanged,  so  that  equilibrium  is  not  disturbed. 
In  any  other  case  the  equilibrium  would  be  affected.  Experiment 
confirms  this  theoretical  conclusion. 

194.  INDUCTION  AND  DEDUCTION. — The  relations  considered 
in  the  last  few  paragraphs  have  a  special  character.  They  have 
been  first  developed  from  other  laws  and  then  tested  by  experi- 
ment. The  laws  used  in  their  development  have,  most  of  them, 
been  discovered  directly  as  generalizations  from  corresponding 


312  FUNDAMENTAL  PRINCIPLES   OF  CHEMISTRY 

experience.  The  process  of  deducing  other  laws  from  those  already 
known  is  called  deduction,  in  distinction  from  induction,  which  is 
the  term  used  to  indicate  the  direct  process.  Deduced  laws  are 
less  certain  than  induced  ones,  for  they  involve  not  only  uncertainty 
in  the  laws  on  which  they  are  based,  but  also  the  possibility  of  error 
due  to  incorrect  or  incomplete  derivation.  They  must  therefore 
be  subjected  to  experimental  proof  by  induction  just  as  the  direct 
laws  are  proven,  that  is,  they  must  be  confirmed  by  generalizations 
from  a  finite  number  of  observations  or  measurements  before  they 
can  take  their  place  as  scientific  laws. 

A  well  justified  question  arises  here.  How  is  it  possible  to  derive 
a  law  from  another  given  law  which  is  different  from  it  ?  A  law 
can  only  include  those  cases  for  which  it  holds,  quite  aside  from 
the  question  of  its  correctness  or  exactness.  The  answer  is  that 
deduced  laws  are  nothing  more  than  special  cases  of  the  laws 
from  which  they  are  derived.  If  our  interest  is  directed  to  the 
question  how  a  special  case  or  group  of  cases,  which  we  know  to  be 
described  by  certain  assumptions,  can  be  brought  under  a  general 
law,  the  answer  frequently  comes  in  such  a  way  that  the  results 
obtained  appear  to  be  completely  new  ones,  and  this  is  because  it 
is  quite  impossible  to  include  in  the  first  statement  and  first  study 
of  the  general  law  all  the  special  cases  which  fall  within  it.  As  we 
become  accustomed  to  apply  such  a  general  law  to  each  special 
case  belonging  under  it,  we  become  so  confident  of  its  value  that 
we  apply  it  to  new  cases,  which  have  not  yet  been  investigated, 
without  any  difficulty,  and  in  fact  quite  unconsciously.  The 
truth  of  the  law  becomes  so  "  self-evident"  that  its  application 
does  not  attract  our  attention,  and  it  is  only  when  the  law  appears 
to  be  "  broken"  that  our  special  interest  is  awakened. 

This  state  of  things  holds  for  the  majority  of  scientists  at  the 
present  time,  as  far  as  the  mechanical  laws,  and  especially  the  law 
of  the  conservation  of  energy,  are  concerned.  We  are  not  yet  so 
thoroughly  accustomed  to  the  manifold  applications  of  the  second 
law  of  energetics,  and  this  is  shown  by  the  fact  that  opinions  are 


REACTION   VELOCITY  AND  EQUILIBRIUM  313 

occasionally  still  put  forward  in  scientific  literature,  which  would, 
if  correct,  indicate  a  breach  of  the  second  law.  On  the  other  hand, 
familiarity  with  the  application  of  this  law  in  certain  fields,  and 
especially  in  general  chemistry,  has  made  many  scientists  so 
thoroughly  familiar  with  its  consequences  that  in  any  special  case, 
whether  it  has  been  treated  by  previous  investigation  or  not,  the 
correct  conclusion  comes  almost  as  a  matter  of  intuition. 

The  history  of  the  development  of  those  laws  which  have  been 
derived  by  deduction  shows  that  they  refer  to  regions  in  which  two 
or  more  laws  are  simultaneously  applicable.  Both  Boyle's  Law 
and  Gay-Lussac's  Law  were  discovered  by  induction.  The  general 
gas  law  PV=RT  was  never  expressed  in  this  form  as  a  result  of 
empirical  reasoning.  It  was  built  up  by  a  combination  of  the  other 
two  laws  and  afterwards  subjected  to  experimental  proof.  In  this 
case  the  regions  covered  by  the  two  individual  laws  are  of  the  same 
extent,  Boyle's  Law  holding  for  all  temperatures  and  Gay-Lussac's 
for  all  pressures  within  which  a  gas  remains  an  approximately 
perfect  one.  The  realm  of  the  combined  law  is  of  the  same  extent. 
In  the  majority  of  cases,  however,  the  regions  described  by  laws 
which  are  combined  for  purposes  of  deduction  only  partially  coin- 
cide, and  under  these  circumstances  the  application  of  the  deduced 
law  is  correspondingly  limited.  The  law  that  catalysers  cannot 
change  equilibrium  is  confined  to  cases  where  chemical  equilib- 
rium is  possible  and  where  we  have  catalysers  for  the  reaction. 
We  derived  it,  however,  from  the  second  law,  which  has  application 
in  numberless  regions  where  neither  chemical  equilibrium  nor 
catalysers  appear. 

While  it  is  true  that  laws  obtained  by  deduction  are  narrower, 
as  far  as  the  region  of  their  application  is  concerned,  it  is  also  true 
that  in  any  case  such  a  law  expresses  more  than  either  of  the  laws 
from  which  it  is  deduced.  In  the  region  where  it  holds  the  state- 
ments which  can  be  made  on  a  basis  of  the  separate  laws  hold 
simultaneously,  and  therefore  the  phenomenon  in  question  is  much 
more  exactly  described  or  determined  than  it  could  be  by  either  of 


314  FUNDAMENTAL  PRINCIPLES  OF  CHEMISTRY 

the  separate  laws  alone.  Each  new  derivation  of  such  a  deduced 
law  opens  the  way  to  a  new  proof  which  shows  whether  or  not  the 
more  general  laws  hold  for  the  special  case  in  question. 

It  is  of  course  possible  that  special  laws  of  this  kind,  which 
result  from  the  simultaneous  application  of  more  general  laws, 
should  be  found  directly  by  experiment  instead  of  being  derived 
by  deduction.  Every  individual  phenomenon  which  we  observe 
and  measure  is  the  subject  of  an  unknown  and  very  large  number 
of  different  laws.  We  express  as  the  result  of  study  a  general  rela- 
tion between  a  number  of  individual  phenomena,  and  our  expres- 
sion of  these  phenomena  determines  how  many  general  laws  are 
included.  The  boundary  between  general  and  special  laws  must 
therefore  be  a  somewhat  indefinite  one.  It  may  easily  happen  that 
a  general  law  and  a  narrower  one  included  within  it  may  be  dis- 
covered experimentally  and  completely  independent  of  each  other. 
It  is  even  possible  that  the  mutual  dependence  may  remain  unrec- 
ognised :  no  one  may  combine  them  consciously  with  the  intention 
of  deducing  a  special  law  from  them.  It  is,  however,  an  important 
task  for  science  to  clear  up  all  such  relations,  and  to  determine 
what  general  laws  are  necessary  and  sufficient  to  include  all  the 
special  laws  involved.  Investigations  of  this  sort  have  been  under- 
taken in  late  years  in  mathematics  and  geometry,  and  they  have 
been  found  difficult.  In  physics  such  a  task  can  only  be  taken  up 
systematically  after  individual  investigations  along  the  same  line 
have  been  at  hand  for  a  long  period.  The  present  book  is  an  ex- 
periment of  the  same  sort  in  chemistry,  or  rather  a  preliminary 
step  in  this  direction. 


CHAPTER  X 

ISOMERISM 

195.  THE  RELATION  BETWEEN  COMPOSITION  AND  PROPERTIES. 
• —  During  an  earlier  period  in  chemistry,  which  lasted  until  about 
the  end  of  the  18th  century,  it  was  possible  to  uphold  the  statement 
that  equality  or  difference  of  properties  and  composition  were 
mutually  determining  facts  definitely  connected  in  every  case.  In 
other  words,  if  substances  were  observed  which  had  different 
properties,  it  was  to  be  concluded  that  they  would  show  differ- 
ences in  composition  under  elementary  analysis.  These  differences 
might  consist  in  differences  in  the  nature  of  the  elements  involved, 
or  at  least  in  differences  in  the  proportions  by  weight  in  which  they 
were  found.  In  the  same  way  the  converse  could  be  asserted,  — 
that  difference  in  composition  corresponds  necessarily  to  difference 
in  properties.  Properties  were  recognised  as  definite  functions  of 
composition. 

One  exception  to  this  statement  was  known,  but  because  of  its 
very  generality  it  was  not  felt  to  be  an  exception.  This  was  the 
set  of  facts  included  in  what  we  call  differences  of  state.  Water, 
ice,  and  steam  are  certainly  substances  having  different  properties, 
and  they  just  as  certainly  have  the  same  composition,  since  they 
can  be  transformed  into  one  another  without  residue.  Hypotheti- 
cal aid  was  made  use  of  in  escaping  from  this  exception,  and  it  was 
assumed  that  the  final  particles  of  these  different  forms  were  alike, 
but  that  they  were  arranged  in  different  ways  with  respect  to  each 
other.  The  name  "  state  of  aggregation"  as  applied  to  these  dif- 
ferences is  an  expression  of  this  assumption.  This  is,  of  course, 
no  explanation  in  the  scientific  sense.  It  merely  transfers  the  fact 

315 


316  FUNDAMENTAL   PRINCIPLES   OF  CHEMISTRY 

to  be  explained  into  a  region  of  hypothetical  cases  which  are  in- 
capable of  proof.  If  it  were  possible,  however,  to  draw  other 
conclusions  which  were  in  agreement  with  experience  from  this 
assumption,  it  would  immediately  become  of  scientific  value,  but 
this  has  so  far  not  been  done  in  this  particular  case.  If  it  could  be 
done  this  assumption  would  be  in  its  effect  equal  to  a  natural  law, 
since  it  would  connect  a  set  of  different  facts  in  a  single  common 
expression.  Until  this  is  done  it  is  better  in  every  way  to  give  up 
such  a  hypothesis. 

What  is,  then,  the  general  difference  between  different  forms  of 
the  same  substance?  The  answer  is  that  their  energy  content  is 
different.  The  difference  is  always  in  such  a  sense  that  gases 
contain  the  most  energy  and  solids  the  least,  the  liquid  state  being 
intermediate  between  them.  As  a  matter  of  form  this  case  can  be 
described  by  considering  energy  as  like  a  chemical  element  differ- 
ing from  all  other  elements  in  having  no  weight.  As  far  as  applica- 
tion of  stochiometric  laws  is  concerned,  we  might  in  this  case  also 
differentiate  between  solutions  and  pure  substances.  We  might 
then  combine  the  various  kinds  of  energy,  heat,  volume  energy, 
etc.,  in  continuously  varying  proportions  with  a  given  amount  of 
substance  by  varying  temperature,  pressure,  and,  in  general,  the 
intensity  of  the  various  energies  freely  and  continuously  in  the  sub- 
stances in  question.  We  could  also  state  a  definite  set  of  relations 
with  respect  to  capacity  factors  of  various  kinds  of  energy,  and 
these  relations  would  be  similar  to  the  stochiometric  ones  (see 
Sec.  170). 

When  we  come  to  the  question  of  differences  of  energy  between 
the  various  states  it  is  necessary  to  consider  whether  it  is  not 
possible,  by  overstepping  the  limits  of  equilibrium,  to  produce 
substances  having  the  same  energy  content  but  differing  in  prop- 
erties. We  may,  for  example,  imagine  water  to  be  subcooled  so 
far  that  its  content  of  energy  is  reduced  to  a  value  equal  to  that 
of  ice.  This  does  not  seem  to  be  possible,  at  least  in  the  simpler 
cases.  Water  cannot  be  subcooled  below  about  -25°;  beyond 


ISOMERISM  317 

that  point  it  freezes.  On  the  other  hand,  it  gives  out  so  much  heat 
when  it  freezes  that  it  could  be  cooled  to  —80°  without  reaching 
the  condition  desired.  In  those  regions  where  we  can  investigate 
subcooling  we  have  not  yet  succeeded  in  producing  water  which 
contains  less  energy  than  ice  at  0°,  where  the  latter  form  has  its 
greatest  energy  content.  The  matter  is  still  less  hopeful  if  condi- 
tions are  compared  at  the  same  temperature ;  for  each  degree  below 
zero  we  must  take  away  from  water  about  double  as  much  heat  as 
from  ice.  If  the  two  are  to  have  the  same  energy  content  at  the 
same  temperature  the  subcooling  would  have  to  be  carried  to  about 
— 160°,  assuming  that  the  values  of  the  specific  heats  are  inde- 
pendent of  temperature. 

For  other  substances  the  difference  in  specific  heat  in  the  solid 
and  liquid  states  is,  in  general,  still  smaller,  and  calculation  will 
show  that  a  still  greater  degree  of  subcooling  would  be  necessary 
to  produce  the  desired  result.  On  the  other  hand,  the  latent  heat 
of  melting  is  often  less  than  for  water.  The  case  discussed  is  one 
that  has  been  so  far  scarcely  examined  at  all,  either  experimentally 
or  theoretically,  and  it  can  therefore  not  be  stated  that  it  is  in  gen- 
eral impossible  to  prepare  two  substances  having  the  same  com- 
position and  the  same  energy  content,  but  exhibiting  different 
properties.  It  might  perhaps  be  possible  to  attain  this  result  in 
such  a  way  that  the  total  energy  would  be  the  same,  but  made  up 
of  various  fractions  of  partial  energies  so  combined  that  the  sums 
are  equal.  In  this  case,  however,  differences  in  the  substances 
could  be  referred  to  differences  in  energy  content,  but  we  should 
be  obliged  to  consider  qualitative  differences  in  energy  in  place  of 
quantitative  ones,  or  in  connection  with  them. 

196.  POLYMORPHISM.  —  Beside  differences  of  state  among  sub- 
stances of  the  same  composition,  we  know  also  of  differences  in 
the  properties  of  such  substances  in  the  same  state.  These  va- 
riations were  first  noticed  among  solid  substances,  and  they 
have  been  given  the  name  of  polymorphism  because  of  the  fact 
that  they  are  most  noticeable  in  differences  in  crystalline  form. 


318  FUNDAMENTAL   PRINCIPLES   OF  CHEMISTRY 

Cases  in  which  amorphous  solids  also  show  this  relation  were 
afterwards  added  to  the  class.  At  the  present  time  we  understand 
by  the  term  "  polymorphism  "  that  solid  substances  can  have  the 
same  composition  but  different  forms,  amorphous  or  crystalline. 
In  these  cases  the  other  properties  —  density,  index  of  refraction, 
colour,  elasticity,  etc.  —  are  also  different. 

Among  these  forms  we  find  that  the  difference  in  energy  content, 
mentioned  above,  always  exists.  A  definite  quantity  of  energy, 
which  usually  appears  as  heat,  is  developed  or  absorbed  in  every 
case  when  a  substance  passes  from  one  of  these  solid  forms  to 
another.  Another  general  peculiarity  holds  here.  Under  given 
conditions  of  temperature  and  pressure  only  one  of  these  forms 
is,  in  general,  stable ;  all  the  others  are  unstable,  and  can  only  be 
produced  with  the  aid  of  phenomena  explained  in  Sec.  63,  and 
by  avoiding  the  presence  of  the  stable  phase.  In  this  case  also 
there  will  be  found  a  corresponding  series  of  temperatures  and 
pressures  at  which  two  phases  can  exist  together,  and  the  appear- 
ance of  a  system  of  three  phases  is  confined  to  single  values  of 
temperature  and  pressure.  This  latter  conclusion  may  be  drawn 
directly  from  the  phase  law. 

These  various  solid  forms  behave,  in  general,  like  the  different 
states  of  a  substance,  and  they  can  best  be  tabulated  by  adding 
them  directly  to  those  states.  The  usual  idea  that  substances  can 
only  exist  in  three  states  must  be  replaced  by  another  permitting 
of  an  unlimited  number.  Among  these  will  usually  be  found 
one  gaseous,  one  liquid,  but  several  solid  forms.  When  a  gas- 
eous substance,  stable  at  high  temperatures,  changes  into  a  liquid 
stable  at  lower  temperatures,  and  in  the  corresponding  change 
from  liquid  to  solid,  heat  is  always  given  out,  and  a  similar  rela- 
tion holds  for  changes  among  the  different  solid  forms  of  a  sub- 
stance. Heat  is  always  generated  during  a  transformation  resulting 
from  decreasing  temperature,  and  vice  versa.  The  sense  of  the 
energy  change  is  governed  in  any  case  by  the  law  of  Sec.  67.  Ac- 
cording to  this  law  that  heat  change  takes  place  which  resists  the 


ISOMERISM  319 

imposed  conditions.  Heat  is  absorbed  during  a  rise  of  tempera- 
ture and  developed  when  temperature  is  lowered  in  all  cases  of 
polymorphic  transformation. 

The  fact  that  a  form  with  greater  energy  content  is  produced 
by  a  rise  of  temperature  is  a  special  case  of  this  general  law.  The 
fact  that  an  increasing  indefiniteness  in  properties  accompanies 
a  change  of  form  which  involves  an  absorption  of  energy  has  not 
yet  been  expressed  in  any  general  law  (the  indefiniteness  men- 
tioned corresponds  to  the  fact  that  liquids  have  no  shape  of  their 
own  and  gases  no  characteristic  volume).  In  place  of  such  a 
general  law  we  have,  so  far,  only  the  hypothesis  concerning  "  state 
of  aggregation." 

197.  THE  DETERMINATION  OF  THE  STABILITY  OF  POLYMOR- 
PHIC FORMS.  —  It  will  be  seen  from  the  above  considerations 
that  within  the  limits  of  the  solid  state  only  one  form  can  exist 
which  is  stable  for  any  given  values  of  temperature  and  pressure. 
If  a  transition  point  happens  accidentally  to  fall  upon  one  of  these 
values  then  two  solid  forms  can  exist  together  in  any  proportions. 
It  might  therefore  be  supposed  that  only  one  of  the  possible  poly- 
morphic forms  would  exist ;  only  the  one,  for  instance,  which  is 
stable  at  ordinary  temperatures.  Experience  shows  the  opposite 
to  be  true.  Many  substances  exist  in  various  forms  under  the 
same  conditions,  and  even  if  they  are  brought  in  contact  in  such 
a  way  that  any  strain  which  might  be  present  would  be  released, 
the  unstable  one  often  remains  unaffected  for  a  longer  or  shorter 
period  of  time. 

The  reason  for  this  is  to  be  sought  in  the  fact  that  the  velocity 
of  such  reactions  among  solid  substances  is  usually  extremely 
small,  and  in  many  cases  it  is  beyond  the  limit  of  observation. 
Even  when  an  unstable  phase  is  brought  in  contact  with  a  stable 
one  they  can  only  touch  each  other  in  a  few  points  because  of 
their  nature  as  solids,  and  the  contact  is  far  from  being  as  perfect 
as  would  be  the  case  between  liquid  and  gaseous  phases  in  con- 
tact with  solids  and  with  each  other.  In  these  cases  it  is  very 


-j 
320  FUNDAMENTAL  PRINCIPLES  OF  CHEMISTRY 

difficult  to  decide  by  direct  observation  which  form  is  the  stable 
one. 

In  this  connection  we  make  use  of  the  reasoning  applied  in 
Sec.  70  to  the  mutual  transformation  of  the  states.  We  found 
that  the  unstable  form  always  exhibits  the  greater  vapour  pres- 
sure, provided  it  can  be  changed  hylotropically  into  the  gaseous 
state.  In  the  cases  in  question  it  would  only  rarely  be  possible  to 
measure  vapour  pressure  directly.  It  is,  however,  evident  that 
a  similar  law  must  apply  to  the  solubility  of  these  substances, 
independent  of  the  solvent  used.  Imagine  each  of  the  solid  forms 
to  be  placed  beside  a  drop  of  the  solvent  at  the  same  temperature. 
Each  drop  of  solvent  would  then  dissolve  the  vapour  of  the  solid 
in  proportion  to  its  pressure  until  equilibrium  was  obtained. 
The  solution  near  the  form  having  the  greater  vapour  pressure 
will  therefore  be  the  most  concentrated  in  the  porportion  of  the 
vapour  pressures.  The  principle  that  a  system  which  is  in  equi- 
librium in  one  sense  must  be  in  equilibrium  in  every  sense  can 
now  be  applied.  The  solutions  which  are  saturated  with  respect 
to  vapour  must  also  be  saturated  with  respect  to  the  solid  phase, 
that  is,  they  would  remain  unchanged  in  direct  contact  with  it, 
and  the  above  principle  follows  directly.  We  may  expand  this 
to  show  that  the  ratio  of  the  concentrations  of  the  two  solutions 
must  be  the  same  as  the  ratio  of  the  vapour  pressures,  at  least 
within  the  range  through  which  Henry's  Law  holds  for  the  sub- 
stances in  question.  The  principle  is  evidently  quite  independent 
of  the  nature  of  the  liquid  used  as  a  solvent. 

The  method  indicated  is  of  general  applicability  in  the  deter- 
mination of  the  comparative  stability  of  the  polymorphic  forms 
of  a  substance,  even  when  the  extreme  slowness  of  transitions  of 
one  state  into  another  prevents  direct  determination. 

198.  ISOMERISM.  —  In  the  majority  of  cases  the  distinction  be- 
tween polymorphic  forms  of  a  given  substance  disappears  when 
they  are  changed  by  fusion  or  solution  into  the  liquid  state,  or  by 
vaporization  into  the  gaseous  state.  This  behaviour  is,  however, 


ISOMERISM  321 

n^t  general,  and  substances  are  known,  which  are  liquids  under 
ordinary  conditions,  which  have  the  same  elementary  composition, 
and  which  still  exhibit  very  great  differences  in  properties.  The 
study  of  the  carbon  compounds,  which  began  about  the  middle 
of  the  last  century,  brought  to  light  a  very  great  number  of  such 
substances,  and  the  systematic  arrangement  of  the  phenomena 
involved  was  of  great  importance  in  the  historical  development 
of  chemical  theory. 

Substances  having  the  same  composition  but  different  proper- 
ties, and  in  which  the  difference  in  properties  persists  in  spite  of 
a  change  of  form,  are  called  isomers.  Polymorphic  substances 
are  only  found  among  solids,  and  the  various  forms  of  a  poly- 
morphic substance  take  on  identical  properties  when  they  are 
transformed  into  gases  or  liquids.  Isomers,  on  the  other  hand, 
exhibit  their  characteristic  differences  in  spite  of  such  changes 
of  state. 

This  statement  holds  only  for  the  two  extremes  which  are 
possible.  A  number  of  isomeric  substances  are  known  which 
behave  in  the  way  mentioned  within  moderate  limits  of  tem- 
perature and  time,  but  in  which  mutual  transformation  takes  place 
at  higher  temperatures  and  after  longer  times.  The  result  is 
finally  a  liquid  or  a  gas  of  definite  properties,  and  the  same  sub- 
stance is  produced  from  any  of  the  isomeric  substances  chosen  as 
starting  point. 

If  the  substance  is  then  brought  back  into  its  original  condi- 
tion, in  which  the  mutual  transformation  takes  place  so  slowly 
that  it  may  be  regarded  as  practically  non-existent,  it  will  be 
found  to  be  a  solution  of  two  or  more  different  substances,  and 
it  may  be  separated  into  its  constituents  by  the  ordinary  means 
(diffusion,  distillation,  crystallization,  etc.). 

It  is  evident  that  this  is  a  case  of  chemical  equilibrium,  and 
one  of  those  in  which  it  is  possible  to  arbitrarily  arrange  for  'con- 
ditions in  which  the  reaction  will  take  place  in  a  reasonable  time. 
It  is  also  possible  to  return  to  other  conditions,  such  that  the  re- 
21 


322  FUNDAMENTAL  PRINCIPLES  OF   CHEMISTRY 

action  velocity  is  practically  zero.  The  case  is  different  in  one 
important  point  from  polymorphism.  Among  isomers  the  normal 
condition,  or  equilibrium,  is  characterized  by  the  fact  that  the 
various  possible  substances  are  all  present  in  mutual  solution, 
while  among  polymorphic  substances  one  form  appears  to  the 
exclusion  of  the  others,  because  of  the  very  limited  solubility  of 
solids.  At  the  transition  points  for  polymers  two  forms  can  exist 
together,  but  here  also  we  find  an  important  difference.  At  the 
transition  points  two  polymorphous  forms  can  exist  together  in 
any  proportion  whatever.  In  a  case  of  equilibrium  between 
liquid  isomers  equilibrium  is  in  any  case  only  possible  at  a  definite 
proportion  between  the  concentrations  of  the  substances  involved, 
and  in  any  case  where  this  ratio  is  not  present  transformation  takes 
place  until  it  is  reached.  Cases  of  isomerism  are  found  in  very 
great  numbers  among  carbon  compounds,  and  this  is  because  of 
two  reasons:  first,  carbon  compounds  are  very  numerous  and 
varied;  second,  they  almost  always  exhibit  an  extremely  small 
reaction  velocity.  This  means  that  we  are  able  to  prepare  and 
observe  forms  which  could  not  be  characterized  as  individual 
substances  if  other  conditions  held. 

The  result  of  this  condition  has  been  that  investigators  have 
studied  these  individual  substances,  unstable  of  themselves,  but 
easy  of  isolation  because  of  their  very  small  reaction  velocities. 
At  the  same  time  only  very  slight  attention  has  been  paid  to  their 
mutual  transformations.  General  reasons  suggest  that  all  of  these 
isomers  can  be  mutually  transformed  so  that  a  single  substance, 
under  the  influence  of  an  accelerator,  would  finally  give  us  a  solu- 
tion of  all  the  possible  isomers.  This  view  is,  however,  unsupported 
by  the  results  of  any  extended  experience,  and  it  must  be  con- 
sidered as  a  deduction  which  still  requires  confirmation  by  ex- 
periment. In  other  words,  we  have  sufficient  scientific  grounds 
for  the  assumption  that  these  substances  are  subject  to  the  general 
laws  of  chemical  equilibrium.  In  only  a  very  few  cases,  however, 
have  actual  equilibrium  conditions  been  investigated,  and  proof 


ISOMERISM  323 

is  therefore  still  necessary  which  will  show  that  no  other  causes 
are  active  which  might  affect  the  application  of  this  law. 

199.  METAMERISM  AND  POLYMERISM.  -  Two  substances  hav- 
ing the  same  chemical  composition  may  differ  in  molar  weight. 
It  is  only  necessary  that  their  molar  weights  should  be  in  rational 
proportion.  If  Aa,  Bb,  Cc, .  .  .  is  the  simplest  formula  which  ex- 
presses the  composition  of  a  substance,  the  molar  weight  of  any 
isomeric  substance  must  be  expressible  by  a  formula  m(AaBbCc), 
in  which  m  is  a  whole  number,  and  the  molar  weights  of  two  such 
substances  must  be  in  the  proportion  m:ml,  that  is  to  say,  in  a 
rational  proportion.  One  of  these  numbers  is  frequently  unity, 
and  then  the  molar  weight  of  the  other  isomeric  substance  is  a 
multiple  of  the  molar  weight  of  the  simple  one.  Because  of  this 
relation  such  substances  are  called  polymers,  and  this  name  has 
been  extended  to  include  isomers  having  different  molar  weights, 
although  it  is  not  strictly  applicable  in  this  case  as  far  as  its 
derivation  is  concerned. 

In  contradistinction  to  these,  isomers  which  have  the  same 
molar  weight  are  called  metameric  substances,  but  this  name  is 
not  in  general  use,  and  the  broader  term  "  isomerism  "  is  usually 
applied  to  cases  of  metamerism  to  distinguish  them  from  those  of 
polymerism.  The  same  general  relations  of  equilibrium  exist  be- 
tween polymers  and  metamers,  and  there  is  no  particular  distinc- 
tion between  them. 

Isomers  share  with  polymorphous  solids  the  property  of  differ- 
ences in  energy  content.  Heat  changes  accompany  their  mutual 
transformation,  and  even  in  the  numerous  cases  where  the  trans- 
formation takes  place  with  such  difficulty  that  the  corresponding 
heat  change  cannot  be  directly  measured,  there  are  general  methods 
of  determining  it.  These  depend  on  the  transformation  of  isomers 
into  a  final  state  which  is  the  same  for  all  of  them  (for  example, 
by  complete  combustion).  Differences  in  the  amounts  of  heat  so 
determined  are  equal  to  the  differences  in  the  energy  content  in 
the  isomers  under  investigation,  for  the  total  energy  difference, 


324  FUNDAMENTAL   PRINCIPLES  OF   CHEMISTRY 

corresponding  to  a  given  original  and  final  condition  of  a  system, 
is  only  dependent  on  this  condition  and  is  not  dependent  on  the 
way  by  which  we  pass  from  one  condition  to  another.  This  is  an 
immediate  consequence  of  the  law  of  the  conservation  of  energy, 
and  if  it  were  not  true  it  would  be  possible  to  create  or  destroy 
any  amount  of  energy  by  causing  the  process  to  take  place  in  one 
direction  and  in  another  way  in  the  opposite  direction.  We  can 
suppose  the  transformation  of  the  isomers  into  their  common,  final 
condition  to  be  so  carried  out  that  the  first  of  the  isomeric  sub- 
stances passes  directly  into  the  final  state.  The  second,  how- 
ever, might  be  first  transformed  into  the  original  condition  of  the 
other  isomer  and  then  into  the  final  condition,  and  the  same  way 
with  the  third,  if  one  existed.  Then  the  heat  change,  correspond- 
ing to  the  transformation  of  the  second  and  third  isomers  into 
the  final  condition,  will  be  made  up  of  the  heats  of  transformation 
of  those  substances  corresponding  to  a  change  into  the  first  isomer, 
and  added  to  these  in  each  case  equal  quantities  of  heat  corre- 
sponding to  the  transformation  from  the  first  into  the  final  condi- 
tion. The  differences  between  these  sums  must  be  equal  to  the 
heat  of  transformation  of  the  other  isomers  into  the  first  one. 

This  reasoning  can  be  expressed  in  symbols  as  follows:  Sup- 
pose the  heats  corresponding  to  the  transformation  of  the  various 
isomers  into  the  final  condition  are  Elf  E2,  E3,  that  the  transfor- 
mation of  the  second  into  the  first  produces  an  amount  of  heat 
equal  to  w2,  that  of  the  third  into  the  first  produces  w3,  etc.,  then 
E2  =  u2+E1;  E3  =  us+E19  etc.,  and  Ez-El  =  u1;  E3-El  =  u39 
which  was  to  be  proven.  It  follows  that  isomeric  substances  can  be 
defined  as  substances  having  the  same  composition  but  different 
energy  content,  and  it  will  be  noticed  that  this  definition  holds 
for  polymorphous  substances  also. 

200.  CONSTITUTION.  —  Let  us  consider  a  special  property, 
with  respect  to  which  isomeric  substances  may  differ.  This  is 
their  tendency  to  form  new  substances  by  chemical  interactions  of 
all  kinds.  Different  products  result  when  the  same  reactions  are 


ISOMERISM  325 

carried  out  on  isomeric  substances  under  the  same  conditions.  In 
this  way  each  individual  substance  of  an  isomeric  group  (there  may 
be  three  or  more  different  substances  of  the  same  composition) 
is  connected  with  a  special  family  of  derivatives  which  are  char- 
acteristic of  this  particular  substance. 

These  facts  have  led  to  the  concept  of  constitution.  We  can 
consider  that  a  part  of  the  elements  present  in  the  various  members 
of  such  a  family  are  the  same  in  each  derivative,  while  the  other 
elements  are  either  removed  by  the  chemical  changes  involved,  or 
else  replaced  by  others.  The  portions  which  remain  constant  are 
termed  radicals,  and  we  try  to  express  all  the  reactions  of  a  sub- 
stance by  saying  that  it  is  made  up  of  the  corresponding  radicals. 
If  two  substances  are  built  up  in  this  way  from  different  radicals, 
so  that  the  sum  total  of  the  combining  weights  of  the  individual 
elements  is  the  same  in  each,  the  result  is  two  substances  of  the 
same  composition  as  far  as  the  elements  are  concerned,  but  dif- 
fering in  the  radicals  contained  in  them.  This  affords  a  so-called 
explanation  for  the  facts  of  isomerism,  especially  for  the  fact  that 
substances  having  the  same  composition  may  possess  different 
properties. 

Such  a  method  of  procedure  has  one  disadvantage.  As  our 
knowledge  of  the  reactions  which  a  substance  can  enter  is  extended, 
it  becomes  necessary  to  increase  the  number  and  complexity  of  the 
radicals  which  we  assume  to  be  present  in  the  compound  in  question. 
Chemists  have  therefore  endeavoured  to  make  the  formulation  of 
such  cases  as  general  as  is  compatible  with  the  aim  before  them. 
The  result  is  the  so-called  structural  theory,  in  which  a  distinct 
difference  is  assumed  between  elements  which  are  directly  bound 
to  each  other  and  those  which  are  indirectly  bound,  that  is,  by 
means  of  other  elements.  All  those  radicals  which  can  be  built 
up  from  the  directly  bound  elements  are  assumed  to  persist  in  the 
compound,  at  least  potentially,  and  this  permits  of  very  general 
application  in  a  great  many  reactions.  As  our  knowledge  of  re- 
actions becomes  more  complete  it  is  found  that  this  auxiliary  fails 


326  FUNDAMENTAL   PRINCIPLES   OF  CHEMISTRY 

in  many  cases.  Especially  where  substances  have  been  investi- 
gated with  great  minuteness  it  has  been  found  that  the  constitution, 
as  based  on  the  above  assumptions,  becomes  less  and  less  certain 
instead  of  more  definite. 

The  definition  of  isomers  as  substances  having  the  same  com- 
position but  different  constitution  offers  no  contradiction  to  our 
previous  definition,  in  which  they  were  said  to  be  substances  of 
the  same  composition  but  differing  in  energy  content.  It  is  very 
reasonable  to  assume  that  differences  in  constitution  will  corre- 
spond to  differences  in  energy.  The  two  definitions  are,  however, 
different,  for  the  one  based  on  energy  content  is  a  purely  experi- 
mental one  and  quite  free  from  doubt.  It  predicts,  however, 
nothing  whatever  about  the  chemical  reactions  which  are  to  be 
expected,  and  is  therefore  not  applicable  as  an  aid  to  building  up 
a  system.  Energy  in  the  sense  in  which  the  word  is  used  here  is 
expressible  by  a  mere  number;  it  has  no  further  properties,  and 
is  therefore  not  of  value  in  expressing  the  qualitative  differences 
belonging  to  chemical  reactions.  The  concept  of  chemical  con- 
stitution was  created  for  this  latter  use,  and  one  of  the  aims  of 
science  will  be  to  give  to  it  a  sharper  and  more  exactly  defined 
meaning  without  in  any  way  decreasing  the  manifoldness  of  its 
applications.  These  will  at  the  same  time  be  extended  and  enlarged. 

201.  VALENCE.  —  The  concept  of  chemical  constitution  in- 
cludes another  important  idea.  The  elements  combine  not  only 
in  the  ratio  of  single  combining  weights,  but  also  in  very  manifold 
proportions  for  which  no  complete  and  regular  principles  have  yet 
been  found,  although  chemical  investigation  has  been  busy  with 
this  problem  for  more  than  half  a  century.  Let  us  first  call  to 
mind  the  facts  in  the  case. 

If  a  chemical  compound  is  subjected  to  a  transformation  by 
which  one  element  is  replaced  by  another,  the  remainder  of  the 
compound  being  unchanged,  this  replacement  can  be  carried  out 
in  various  ways.  The  elements  may  replace  each  other  in  the  ratio 
of  their  combining  weights,  so  that  the  number  of  combining 


ISOMERISM  327 

weights  remains  unchanged,  or  in  place  of  the  ratio  1:1  we  may 
find  other  ratios,  1:2,  1:3,  2:3,  etc.  Those  elements  which  are 
never  replaced  by  more  than  one  combining  weight  of  another 
element  are  set  aside  and  said  to  be  univalent.  They  exhibit,  of 
course,  the  inverse  of  this  property,  and  more  than  one  combining 
weight  of  one  of  these  elements  replaces  a  single  combining  weight 
of  certain  other  elements.  The  number  so  determined  is  used  in 
characterizing  the  other  elements  as  possessing  valences  correspond- 
ing to  the  number  of  combining  weights  of  the  univalent  elements 
which  must  be  used  to  replace  one  combining  weight.  By  this 
classification  we  have  bivalent,  trivalent,  quadrivalent,  etc.,  ele- 
ments. The  highest  valence  which  we  have  so  far  been  obliged  to 
assume  is  8,  but  there  is  no  real  reason  why  we  should  not  go 
higher  if  necessary. 

Valences  of  the  various  elements  are  so  chosen  that  in  chemical 
compounds  each  valence  is  active.  If  two  univalent  elements 
are  concerned  this  can  only  be  expressed  in  one  way.  The  valence 
of  each  of  the  elements  is  connected  with  the  valence  of  the  other, 
and  the  two  valences  are  said  to  be  mutually  "  saturated."  In  the 
same  way  one  combining  weight  of  a  bivalent  or  polyvalent  element 
can  only  be  combined  in  one  way  with  a  corresponding  number  of 
combining  weights  of  a  univalent  element.  But  where  two  com- 
bining weights  of  a  trivalent  element  combine  with  three  combin- 
ing weights  of  a  bivalent  one,  six  valences  are  to  be  disposed  of, 
and  in  this  case  three  different  arrangements  are  possible  by  which 
the  elements  are  made  to  appear  as  combined  in  three  different 
ways.  In  order  to  make  this  clear  we  will  make  use  of  a  method 
of  expression  which  has  become  general  in  chemistry.  The  number 
of  valences  will  be  indicated  by  a  corresponding  number  of  strokes 
emanating  from  the  symbol  of  the  element.  If  A  is  the  bivalent 
and  B  the  trivalent  element,  the  following  structures  are  possible : 

/A\  /A  A-A-A 

B-A-B  A=B-B    |  \        / 

\A  B=B 


328  FUNDAMENTAL  PRINCIPLES  OF  CHEMISTRY 

It  will  be  seen  that  all  the  valences  are  active  or  saturated.  Each 
A  has  two  strokes,  and  each  B  has  three,  and  none  of  these  strokes 
is  left  unconnected  with  another  element. 

It  is  evident  that  this  schematic  representation  contains  a  theory 
of  isomerism  which  is  in  general  agreement  with  the  one  given 
above,  for  it  affords  a  means  of  expressing  either  direct  or  indirect 
combination  between  elements.  The  three  structures  given  above 
are  all  different  in  a  definite  sense,  and  the  question  arises  whether 
such  differences  in  valence  diagrams  correspond  to  constitutional 
differences  in  chemical  compounds  and  to  related  differences  in 
their  chemical  reactions. 

The  answer  is  that  such  a  representation  of  the  facts  is  in  general 
possible,  but  at  the  same  time  a  considerable  degree  of  uncer- 
tainty and  incompleteness  still  remain.  Such  relations  are  there- 
fore to  be  considered  rather  as  rules  with  a  considerable  number  of 
exceptions  than  as  natural  laws  to  which  no  exceptions  exist.  It 
must  first  be  questioned  whether  the  valence  concept  can  be  carried 
out  so  strictly  that  a  definite  valence  can  be  ascribed  to  each  ele- 
ment, by  means  of  which  all  of  its  compounds  can  be  represented. 
The  answer  is  that  this  is  in  general  impossible.  Each  element 
has,  to  be  sure,  a  principal  valence  according  to  which  the  majority 
of  its  compounds  is  made  up,  but  almost  all  elements  form  com- 
pounds with  univalent  elements,  in  which  they  are  present  in  vary- 
ing proportion,  and  this  means  that  a  varying  number  of  valences 
must  be  active.  In  order  to  show  in  such  a  case  which  valence  is 
to  be  used  in  the  representation  of  a  given  compound,  further  data 
is  necessary.  This  data  is  in  many  cases  available,  for  the  prop- 
erties of  compounds  are  dependent  upon  the  valences  involved, 
and  measurement  of  properties  enables  us  to  determine  the  valence 
to  be  used  in  describing  this  particular  compound.  Different  prop- 
erties usually  give  the  same  result  when  investigated  in  this 
way,  but  apparent  contradictions  occasionally  occur.  This  fact 
is  to  be  regarded  as  a  sign  that  the  scientific  statement  of  the 
facts  in  question  is  not  given  with  sufficient  accuracy  by  the 


ISOMERISM  329 

scheme  we  have  used  to  represent  it  (in  this  case  the  use  of 
valences). 

It  must  therefore  be  inquired  whether  the  experimentally  dis- 
covered cases  of  isomerism  correspond  in  number  and  constitution 
to  those  which  are  indicated  by  the  schematic  representation  em- 
ployed. In  general,  the  number  of  experimentally  known  cases 
of  isomerism  is  smaller  than  the  theoretically  possible  number, 
and  this  is  to  be  expected,  for  it  is  hardly  possible  that  the  experi- 
mental possibilities  would  already  be  exhausted.  But  from  time 
to  time  cases  have  appeared  where  experimental  isomers  have  been 
found  in  larger  number  than  would  be  indicated  by  the  theory. 
This  necessitates  the  introduction  of  a  new  factor  into  the  theory, 
for  example,  one  involving  differences  in  the  spatial  arrangement 
of  elements,  and  in  a  few  cases  even  this  assumption  appears  insuf- 
ficient. All  of  these  questions  are  most  important  in  the  study  of 
carbon  compounds,  for  it  is  in  this  branch  of  chemistry  that  the 
number  and  variety  of  isomers  is  by  far  the  greatest.  In  this 
great  group  of  compounds  a  systematic  arrangement  and  a  theory 
of  isomers,  together  classed  under  the  name  of  structure  theory, 
which  has  been  developed  on  the  basis  of  valence,  has  proven  itself 
a  very  important  aid.  In  this  system  it  has  been  possible  to  give 
to  carbon  a  constant  valence  of  4  in  the  majority  of  cases.  It  has 
never  been  found  necessary  to  give  it  a  greater  valence,  but  cases 
have  appeared  in  which  valences  of  2  and  3  might  lead  to  a  better 
representation  of  the  actual  relations. 

The  relation  between  the  theory  of  valence  and  the  molar  con- 
cept deserves  special  mention.  It  is  evident  from  the  following 
diagram  that  the  valences  of  a  single  bivalent  element  cannot  be 
saturated  by  those  of  a  trivalent  one.  If,  however,  we  use  polymers, 
there  is  no  difficulty  in  taking  care  of  the  valences,  and  this  is  shown 
below  for  the  case  where  the  molar  weight  has  double  the  simple 

Value"  A-B-B-A. 

An  assumption  of  this  sort  is  demanded  by  the  structural  theory, 


330  FUNDAMENTAL  PRINCIPLES  OF  CHEMISTRY 

and  it  has  been  agreed  that  molar  formulae  are  to  be  used  as  the 
basis  for  structural  diagrams.  Mutual  saturation  of  the  valences 
is  demanded  for  the  corresponding  number  of  combining  weights 
of  the  various  elements.  Determination  of  the  molar  weight  is 
therefore  a  matter  of  the  greatest  importance  for  all  those  questions 
which  involve  structural  theory,  and  especially  for  isomerism  and 
constitution. 


CHAPTER  XI 

THE   IONS 

202.  SALT  SOLUTIONS  AND  IONS.  —  The  majority  of  substances 
recognised  by  chemistry  can  be  described  by  the  laws  which  we 
have  developed,  and  they  need  no  further  fundamental  assumptions 
in  their  scientific  treatment.  There  is,  however,  a  large  and  im- 
portant group  of  substances  in  which  regular  contradictions  to 
those  laws  appear,  and  these  are  not  pure  substances  but  a  definite 
set  of  solutions.  Especially  among  the  aqueous  solutions  of  salts 
we  will  find  it  necessary  to  extend  our  general  ideas.  The  con- 
tradictions mentioned  are  most  apparent  in  this  class  of  substances, 
and  they  can  also  be  most  satisfactorily  explained  in  connection 
with  them.  First  of  all  we  must  have  an  experimental  definition  of 
the  concept  "  salt."  A  salt  is  a  substance  whose  solutions  act  as 
conductors  of  electricity  of  the  second  class.  This  definition  has 
the  advantage  of  simplicity  and  clearness,  but  it  has  at  the  same 
time  the  disadvantage  that  it  depends  upon  the  application  of 
electrical  energy.  This  form  of  energy  has  numerous  relations  to 
chemical  energy,  but  it  is  unquestionably  different  from  the  latter. 
A  chemical  definition  of  a  salt  may  be  given  as  follows:  A  salt 
is  a  substance  which  has  the  properties  of  a  pure  substance  in  the 
undissolved  condition,  while  it  exhibits  the  properties  of  two  dif- 
ferent substances  while  it  is  in  solution.  Both  definitions  will  be 
considered  exhaustively  in  the  following  pages. 

By  a  conductor  of  the  second  class  is  to  be  understood  a  sub- 
stance in  which  chemical  reaction  takes  place  at  the  points  where 
the  electric  current  enters  and  leaves  it,  and  having  the  further 
characteristic  that  the  amount  of  chemical  action  is  proportional 

331 


332  FUNDAMENTAL  PRINCIPLES   OF  CHEMISTRY 

to  the  amount  of  electricity  which  passes.  In  other  words,  an  elec- 
tric current  cannot  pass  through  such  a  conductor  without  at  the 
same  time  causing  decomposition.  A  reasonable  description  of  the 
facts  may  be  based  upon  the  assumption  that  the  passage  of  the 
electric  current  is  accompanied  by  the  simultaneous  motion  of 
certain  constituents  of  the  solution.  These  are  the  ions,  and  the 
action  takes  place  in  such  a  way  that  negative  electricity  moves 
with  one  of  the  constituents  of  the  salt,  while  positive  electricity 
moves  with  the  other.  The  first  constituent  is  called  the  anion, 
the  second,  the  cation  of  the  salt.  The  places  where  the  current 
enters  and  leaves  are  called  the  electrodes,  and  a  substance  which 
conducts  in  this  way  with  simultaneous  separation  of  its  constitu- 
ents is  called  an  electrolyte.  The  simplest  case  is  one  in  which 
the  salt  consists  of  two  elements,  neither  of  which  reacts  with  the 
solvent  in  the  free  state.  They  are  therefore  not  influenced  by  the 
solvent,  and  the  elements  appear  at  the  electrodes  while  the  cor- 
responding quantity  of  electricity  passes  on  through  the  circuit. 
The  elements  within  the  electrolyte  are  in  some  way  connected 
with  this  quantity  of  electricity,  and  in  this  condition  they  exhibit 
properties  quite  different  from  those  belonging  to  their  ordinary 
condition,  that  is,  belonging  to  their  condition  after  the  quantity 
of  electricity  has  left  them.  This  difference  becomes  evident  when 
the  elements  give  up  their  electricity  at  the  electrodes,  for  at  these 
points  they  appear  in  their  ordinary  condition.  It  must  be  con- 
cluded that  they  possess  other  properties  as  long  as  they  are  con- 
nected with  the  corresponding  quantities  of  electricity.  During 
the  process  heat  effects  are  produced  at  the  electrodes,  and  counter 
electro-motive  forces  are  produced  which  can  only  be  overcome  by 
the  expenditure  of  energy  from  the  current.  The  passage  of  ions 
of  a  salt  into  the  ordinary  condition  is  therefore  accompanied  by 
energy  changes.  We  have  already  given  a  name  to  substances 
having  the  same  composition  but  exhibiting  different  properties 
and  different  energy  contents.  These  we  have  called  isomers,  and 
in  this  sense  of  the  word  ions  and  elements  having  the  same  com- 


THE   IONS  333 

position  may  be  included  in  the  same  class.  The  electrical  differ- 
ences between  ions  and  ordinary  neutral  substances  indicate  that 
this  form  of  isomerism  is  even  more  complicated  than  the  other. 
It  may  be  characterized  by  the  term  "  electrical,"  or  even  better 
"  electrolytic,"  isomerism  to  indicate  its  close  connection  with  elec- 
trical' phenomena. 

203.  FARADAY'S  LAW.  —  Salts  in  the  solid  state  behave  like 
neutral,  unelectrified  substances.  It  is  a  well-known  principle  of 
physics  that  only  equal  amounts  of  electricity  of  opposite  signs 
can  be  produced  simultaneously,  and  it  follows  from  this  that  the 
quantities  of  electricity  which  are  connected  with  the  two  ions  of  a 
salt  in  solution  must  be  equal  and  of  opposite  sign.  If  amounts  of 
various  salts,  each  of  which  contains  the  same  amount  of  any 
particular  ion,  are  compared,  it  follows  that  the  quantity  of  elec- 
tricity which  is  connected  with  the  other  ions  must  be  in  every 
case  the  same,  and  this  reasoning  holds  for  cations  and  for  anions 
as  well.  It  follows  that,  in  general,  equivalent  amounts  of  different 
ions  are  connected  with  the  same  amount  of  electricity.  When 
they  can  combine,  those  anions  will  be  equivalent  which  combine 
with  the  same  amount  of  any  cation,  and  cations  will  be  equivalent 
which  combine  with  the  same  amount  of  any  anion.  The  quantity 
of  electricity  in  each  of  these  cases  will  be  the  same,  and  the  signs 
will  be  found  in  the  proper  relation.  A  cation  is  equivalent  to  an 
anion  if  it  forms  a  neutral  salt  with  it.  Each  is  connected  with  the 
same  quantity  of  electricity  of  different  sign,  and  the  salt  will  be 
neutral.  The  quantities  involved  are  given  by  the  law  of  the  com- 
bining weights,  and  the  conclusion  is  that  equal  quantities  of 
electricity  are  connected  either  with  one  combining  weight  of  any 
ion,  or  a  rational  fraction  of  the  combining  weight.  This  last 
statement  is  necessary  because  elements  combine  to  form  a  salt 
not  only  in  the  ratios  of  their  combining  weights  but  also  in  other 
proportions  as  1 :  2,  1 :  3,  2 :  3,  etc. 

This  law  exhibits  itself  in  a  special  way  when  ions  separate  from 
the  electrolyte  during  electrolysis.  Under  these  circumstances 


334  FUNDAMENTAL  PRINCIPLES   OF  CHEMISTRY 


chemically  equivalent  amounts  of  the  different  ions  are  separated 
in  connection  with  the  passage  of  the  same  quantity  of  electricity. 
While  the  quantity  of  electricity  is  in  each  case  the  same,  the  work 
required  may  be  very  different  in  different  cases,  since  electrical 
energy  is  the  product  of  quantity  of  electricity  by  potential  differ- 
ence. Differences  in  the  latter  factor  determine  differences  in  the 
amount  of  work  which  accompanies  the  transformation  of  ions 
into  electrically  neutral  isomeric  substances. 

This  law,  which  states  that  chemically  equivalent  amounts  of 
ions  or  their  transformation  products  separate  from  any  salt  solu- 
tion, or  in  general  from  any  electrolyte,  in  connection  with  the 
same  quantity  of  electricity,  was  discovered  by  Faraday,  and  it 
is  called  Faraday's  Law.  Before  he  arrived  at  this  law  Faraday 
showed  that  the  quantity  of  substance  separated  is  proportional 
to  the  quantity  of  electricity  which  passes,  and  this  is  of  course 
a  necessary  premise  for  the  statement  of  the  general  law. 

The  derivation  which  we  have  just  given  for  Faraday's  Law 
depends  upon  the  fact  that  electric  neutrality  is  preserved  as  a  mat- 
ter of  experiment  throughout  all  transformations  which  take  place 
between  salts.  Measurements  on  Faraday's  Law  have  also  shown 
that  a  very  large  quantity  of  electricity  is  connected  with  a  com- 
paratively small  amount  of  substance  in  the  form  of  ion,  and  the 
fact  that  no  free  electricity  ever  appears  when  salts  react  affords 
an  exceedingly  sensitive  proof  of  the  quantitative  accuracy  of 
Faraday's  Law. 

204.  THE  CONCEPT  OF  IONS  CONSIDERED  CHEMICALLY.  —  Salts 
were  defined  above  (Sec.  202)  as  substances  which  behave  like 
pure  substances  when  in  the  pure  state,  but  which  show  reactions 
of  several  constituents  when  in  solution.  These  constituents  are 
the  ions,  which  have  just  been  defined  in  terms  of  their  electrical 
properties. 

Let  us  consider  two  salts  A1B1  and  AJ$^  the  constituent  Al 
being  the  same  in  each,  the  other  constituent  B1  or  B2  being  differ- 
ent. These  two  salts  are  different  substances,  each  possessing  its 


THE  IONS  335 

own  properties.  If  these  salts  are  dissolved  in  water  a  part  of 
the  properties  of  their  solutions  will  be  in  agreement,  while  another 
part  will  differ.  Careful 'investigation  shows  that  the  properties 
of  these  solutions  can  be  in  every  case  described  as  a  sum,  a  part 
of  which  depends  on  the  constituent  Al  and  another  part  on  the 
constituent  B.  These  two  constituents  were  combined  in  the  orig- 
inal salt,  but  in  the  limiting  case,  that  of  very  great  dilution  of 
the  solution,  this  fact  has  no  bearing  whatever.  The  two  solu- 
tions, one  made  of  A1B1  and  the  other  of  AJE}^  are  alike  as  far 
as  the  constituent  Al  is  concerned,  and  different  as  far  as  the  other 
constituent  B A  or  B 2  is  concerned. 

These  differences  and  points  of  agreement  hold  for  physical 
properties  as  well  as  for  chemical  ones.  If  the  constituent  B^  has 
a  definite  colour  of  its  own,  the  same  colour  will  be  characteristic 
of  all  dilute  salt  solutions  containing  the  constituent  Blt  quite  in- 
dependent of  the  nature  of  the  other  constituent  A.  Even  when 
A  has  a  colour  of  its  own  the  colour  of  the  salt  solution  containing 
the  two  coloured  constituents  will  be  found  to  be  the  sum  of  the 
two  individual  colours,  that  is  to  say,  each  of  the  constituents  ex- 
hibits its  characteristic  absorption  for  light  independent  of  the 
effect  of  the  other. 

In  the  same  way  any  definite  chemical  property,  such  as  the 
capacity  to  form  a  precipitate  with  another  substance,  will  be 
found  in  all  salt  solutions  which  contain  a  common  constituent  A 
or  B.  Even  the  physiological  and  medicinal  effects  of  salts  have 
been  found  to  be  independent  of  one  of  their  constituents,  and  if 
the  medically  active  constituent  is  present  in  the  salt,  the  other 
constituent  may  be  anything  whatever,  provided  it  exhibits  no 
medicinal  effect  of  its  own. 

This  peculiarity  is  found  among  salts  containing  two  elements 
and  also  among  those  having  more  constituents.  We  may  there- 
fore draw  a  conclusion  similar  to  that  found  for  composition  and 
electrolytic  conductivity.  The  independent  effects  found  in  binary 
salts  belong  to  the  independent  constituents  of  the  salt.  If  more 


336  FUNDAMENTAL   PRINCIPLES  OF  CHEMISTRY 

complicated  compounds  are  in  question,  these  are  compared  with 
binary  salts  having  a  constituent  in  common  with  the  more  com- 
plex one. 

All  ions,  without  exception,  combine  with  each  other  to  form 
salts,  and  it  is  therefore  always  possible  to  prepare  a  salt  one  of 
whose  ions  is  familiar.  The  composition  and  properties  of  the 
other  ion  can  then  be  determined,  and  in  this  way  it  is  possible 
to  investigate  salts  of  any  composition  whatever. 

The  question  arises  whether  the  chemical  definition  of  a  salt 
leads  to  results  which  are  in  agreement  with  the  electrical  defini- 
tion when  we  apply  them  both  to  various  substances.  The  an- 
swer is  in  the  affirmative.  Substances  which  conduct  electrolytically 
contain  constituents  which  react  independently  and  vice  versa. 
In  this  case,  as  in  all  others,  we  find  cases  in  which  the  conductiv- 
ity is  very  small,  and  in  which  therefore  the  independent  part  of 
the  salt  is  also  small.  Such  cases  require  more  exhaustive  treat- 
ment than  can  be  given  here,  and  they  are  therefore  only  mentioned 
to  prevent  any  tendency  to  overmuch  formal  deduction  from  the 
laws  given. 

205.  UNIVALENT  AND  POLYVALENT  IONS.  —  Salts  are  subject 
to  the  general  rules  of  valence.  Polyvalent  elements  combine  with 
the  corresponding  number  of  univalent  ones  to  form  salts,  and 
these  salts  break  up  into  univalent  or  polyvalent  ions.  Measure- 
ments based  on  Faraday's  Law  have  shown  that  96,540  units  of 
electrical  quantity  (coulombs)  correspond  to  one  combining 
weight  of  a  univalent  ion.  With  each  combining  weight  of  an 
n-valent  ion  n  X  96,540  coulombs  will  therefore  be  connected,  and 
this  conclusion  depends  upon  the  law  of  equivalents.  It  follows 
in  the  same  way  that  one  combining  weight  of  an  w-valent  ion 
combines  with  n  combining  weights  of  any  univalent  ion  to  form 
a  salt. 

This  definite  relation  between  quantity  of  electricity  and  com- 
bining weights  gives  rise  to  a  new  kind  of  isomerism  among  ions. 
Composition,  molar  weight,  and,  as  far  as  we  know,  constitution 


THE  IONS  337 

also  are  in  agreement  among  the  isomers,  but  the  quantity  of 
electricity  which  is  connected  with  a  mol  may  be  different  in 
different  cases.  The  letter  F  is  used  to  indicate  96,540  coulombs, 
and  the  isomerism  just  mentioned  may  be  expressed  by  connect- 
ing various  integral  values  of  F  with  the  same  element  or  complex 
of  elements. 

Beside  this  kind  of  isomerism  ions  can  exhibit  the  constitutional 
isomerism  already  described  (Sec.  200),  and  this  differs  from 
electrical  isomerism  in  that  ions  usually  preserve  their  valence  in 
the  different  forms.  "  Those  ions  which  show  constitutional  isom- 
erism are  portions  of  salts  exhibiting  constitutional  isomerism, 
and  this  condition  may  appear  for  both  cation's  and  anions. 

It  is  a  matter  of  experience  that  the  great  majority  of  ions  are 
u  nivalent  or  bivalent.  Trivalent  ions  and  those  of  higher  valence 
are  comparatively  rare,  and  appear  more  frequently  in  complicated 
compounds  than  in  simple  ones.  Four  valences  appears  to  be  the 
limit  among  elementary  ions,  and  in  fact  the  existence  of  quad- 
rivalent ions  is  doubtful. 

206.  THE  MOLAR  WEIGHT  OF  SALTS.  —  Those  solutions  which 
conduct  electrolytically  exhibit  remarkable  properties  when  we 
try  to  determine  the  molar  weight  of  the  salt  in  them  by  the  methods 
of  Sections  176  et  seq.  The  molar  weight  so  determined  is  in  all 
cases  too  small.  Confining  ourselves  for  the  present  to  very  dilute 
solutions  (more  concentrated  ones  will  be  taken  up  later),  it  ap- 
pears that  the  salts  which  are  made  up  of  two  univalent  ions  give 
a  molar  weight  one  half  as  great  as  that  which  might  be  expected 
from  their  formula?.  If  the  salt  is  made  up  of  one  bivalent  and  two 
univalent  ions,  its  molar  weight  seems  to  be  only  one  third  that 
given  by  the  formula,  and  in  general  it  appears  as  a  fraction  de- 
termined by  the  number  of  ions  into  which  the  salt  can  break  up. 

These  facts  may  be  explained  with  the  aid  of  the  assumption 
which  we  made  in  considering  the  electrical  and  chemical  prop- 
erties of  salt  solutions.  This  was  that  ions  exist  as  independent 
substances  in  salt  solutions.  One  mol  of  the  salt  containing  two 
22 


338  FUNDAMENTAL   PRINCIPLES   OF  CHEMISTRY 

univalent  ions  produces  two  mols  of  ions,  and  must  therefore  exert 
double  the  osmotic  pressure,  etc.  If  we  therefore  calculate  molar 
weight  with  the  premise  that  no  separation  into  ions  has  taken 
place,  it  is  found  too  small  by  one  half.  We  must  in  general  expect 
to  find  that  fraction  of  the  molar  weight  of  the  salt  which  is  deter- 
mined by  the  number  of  mols  of  ions  which  can  be  produced  from 
the  salt,  and  experiment  confirms  this. 

These  facts  are  in  complete  agreement  with  the  chemical  and  * 
electrical  ones  already  mentioned.     They  form  the  principal  basis 
for  the  idea  that  salts  in  conducting  solutions  are  subject  to  elec- 
trolytic cleavage  or  dissociation,  and  this  idea  was  first  expressed 
by  Arrhenius  in  1887. 

207.  THE  APPLICATION  OF  THE  PHASE  LAW.  —  In  accordance 
with  the  facts  and  relations  just  given,  a  salt  solution  must  be  con- 
sidered a  ternary  system  in  the  sense  of  the  phase  law,  even  though 
we  made  the  solution  from  a  single  salt  and  water;  that  is,  from 
two  constituents.  If  the  number  of  degrees  of  freedom  of  such  a 
system  be  investigated,  it  will  be  found  to  act  like  a  solution  which 
contains  two  dissolved  substances.  It  has  only  three  degrees  of 
freedom  when  no  other  phase  except  the  liquid  is  present,  and  a 
correspondingly  smaller  number  when  several  phases  exist  together. 

If  two  salts  are  brought  together  in  a  solution  further  complica- 
tions result.  In  some  cases  the  system  behaves  as  though  it  con- 
tained three  components,  and  in  others  as  though  it  contained  four. 
In  no  case,  however,  does  it  appear  to  contain  five  constituents, 
and  this  would  necessarily  be  the  case  if  any  salt  added  two  inde- 
pendent constituents  to  the  solution. 

It  can  be  shown  that  the  effective  influence  may  be  referred  to 
three  constituents  or  to  four,  depending  on  whether  or  not  the 
two  salts  contain  the  same  ion.  If  they  do,  three  constituents  are 
active.  If  they  do  not,  four  constituents  appear.  In  other  words, 
the  number  of  ions  present,  together  with  the  water,  determine  the 
result,  but  we  find  one  less  degree  of  freedom  than  would  be  cal- 
culated from  the  number  of  ions  arid  the  solvent. 


THE   IONS  339 

This  means  that  one  of  the  degrees  of  freedom  has  already  been 
taken  care  of  under  these  circumstances,  and  it  is  evident  that 
this  depends  upon  the  fact  that  the  amounts  of  the  various  ions  are 
not  independent  of  each  other.  Their  amounts  must  be  such  that 
the  total  quantity  of  anions  i$  equivalent  to  that  of  cations.  If  one 
of  the  ions  were  present  in  excess  a  corresponding  and  very  large 
amount  of  electric  charge  would  appear.  Electric  neutrality,  or, 
what  is  the  same  thing,  chemical  equivalence,  must  exist  between 
the  anions  and  the  cations.  The  fulfilment  of  this  condition  cor- 
responds to  the  disposal  of  one  of  the  possible  degrees  of  freedom, 
and  one  less  remains  for  other  changes. 

Viewed  from  this  standpoint  it  is  possible  to  show  agreement 
between  the  behaviour  of  salt  solutions  and  the  statement  of  the 
phase  law.  We  may  state  this  in  the  following  rule :  The  various 
ions  are  to  be  considered  as  independent  constituents,  and  one  is 
to  be  subtracted  from  the  sum  of  freedoms  and  phases  resulting 
from  the  corresponding  enumeration. 

This  gives  us  a  clue  to  the  fact  that  a  solution  of  a  single  salt 
behaves  like  a  single  substance.  The  solution  contains  three  in- 
dependent constituents,  —  solvent  and  two  ions.  If  we  have  only 
one  phase  3+2—1=4  degrees  of  freedom  must  obtain.  As  a 
matter  of  fact  three  only  will  be  found  in  any  case,  as  indicated  by 
the  above  rule.  The  actual  number  of  degrees  of  freedom  is  in 
agreement  with  the  number  which  would  belong  to  the  solution 
of  a  single  substance,  and  the  earlier  idea  that  salts  were  to  be  con- 
sidered as  individual  substances,  even  when  they  were  in  solution, 
has  its  justification  in  this  fact.  Deviation  from  the  phase  law  only 
appears  when  several  salts  are  present  in  a  solution,  and  the  ap- 
pearance of  this  deviation  is  a  further  reason  for  considering  ions 
as  independent  constituents  of  salt  solutions. 

208.  ELECTROLYTIC  DISSOCIATION.  —  The  transformation  of 
a  salt  into  its  ions  within  a  solution  is  called  electrolytic  dissocia- 
tion, and  this  process  is  a*  chemical  reaction  coming  under  the 
general  laws  already  discussed.  A  salt  solution  gives  back  the 


340  FUNDAMENTAL   PRINCIPLES   OF   CHEMISTRY 

original  salt  unchanged  when  it  is  evaporated,  and  this  proves 
clearly  that  the  dissociation  into  ions  is  reversed  when  the  salt 
separates.  The  question  arises  whether  dissociation  is  complete 
within  the  solution  or  not.  In  other  words,  does  a  quantitative 
equilibrium  exist  between  the  unchanged  salt  and  its  ions? 

The  answer  is  in  the  affirmative.  It  is  precisely  because  such 
a  finite  equilibrium  usually  exists  that  the  simple  relations  of 
Sec.  206  must  be  confined  to  very  dilute  solutions.  When  a  salt 
breaks  up  into  its  ions,  a  corresponding  increase  in  osmotic  pres- 
sure accompanies  the  increase  in  the  molar  concentration  of  the 
solution,  and  if  the  osmotic  pressure  is  forcibly  changed  by  dilu- 
tion or  concentration,  reactions  will  be  set  up  which  resist  the 
change.  If  concentration  takes  place  and  the  osmotic  pressure  is 
forcibly  increased,  that  reaction  will  take  place  which  tends  to 
diminish  the  pressure,  and  if  dilution  is  brought  about  the  re- 
action will  take  place  which  increases  the  pressure.  The  first  of 
these  reactions  consists  in  the  formation  of  undissociated  salt,  the 
second  reaction  in  more  complete  dissociation.  Concentration  of 
a  salt  solution  therefore  leads  finally  to  the  separation  of  the  salt 
in  the  solid,  undissociated  form,  while  dilution  leads  finally  to  a  com- 
plete dissociation  into  ions.  Between  these  two  limits  equilibrium 
corresponding  to  the  general  law  of  mass  action  will  exist. 

In  the  simplest  case  in  which  two  univalent  ions  make  up  a  salt, 
this  may  be  expressed  as  follows:  K  is  the  cation,  A  the  anion, 
S  the  salt,  and  the  equation  for  the  reaction  will  be  K  +  A  =S.  If 
k,  a,  and  s  are  the  concentrations  of  these  substances  the  equili- 
brium equation  is  -  —  =  C.  The  equation  is  based  on  one  mol  of 
s 

the  salt,  and  we  will  let  x  be  the  fraction  of  this  mol  which  is  broken 
up  into  ions;  then  l—x  would  be  the  unchanged  portion,  and 
we  will  use  v  for  the  total  volume.  The  concentrations  are  then 

a  =  -,  k  =  -,  and  s  =  - .    Substituting  these  in  the  equilibrium 

x2 
equation,  we  have  —      —  =  C. 


THE   IONS  341 

This  equation  was  first  suggested  by  Ostwald  in  1888,  and  it 
represents  the  general  behaviour  of  electrolytes  in  a  qualitative 
way.  In  regions  of  small  and  medium  dissociation  it  has  quantita- 
tive accuracy.  Ir  the  limiting  case  of  more  complete  dissociation 
deviations  occur  which  have  not  yet  been  fully  cleared  up.  If  v 
is  very  large,  which  is  the  case  for  unlimited  dilution,  x  approaches 
unity  and  1  —  x  approaches  zero ;  that  is,  the  dissociation  is  com- 
plete. The  constant  C  has  an  individual  value  for  each  electrolyte 
or  salt,  and  it  frequently  shows  relations  to  composition  and 
constitution. 

In  cases  where  a  larger  number  of  different  ions  are  present  in 
a  solution  the  law  of  mass  action  is  still  applicable,  and  a  large 
number  of  various  phenomena  characteristic  of  ions  may  be 
represented  by  its  use.  This  application  does  not,  however,  lead 
to  anything  new  or  of  fundamental  importance,  and  the  simple 
example  given  is  therefore  sufficient  to  make  the  existing  relations 
clear. 


INDEX 


A. 


Absolute  temperature,  43 
Absolute  weight,  10 
Absolute  zero,  43 
Absorption 

law  of,  121 
Allotropic  forms 

vapour  pressure  of,  93 

solubility  of,  161 
Allotropism,  89 
Amorphous  bodies,  28 
Analysis 

elementary,  172 
Analytical  chemistry,  245 
Analytical  processes,  168,  233 
Anion,  332 

Anomalous  behaviour  of  gases,  307 
Arbitrary  properties,  3 
Atmosphere,  17 
Atomic  weight,  272 


B. 

Balance,  equal  arm,  11 
BERTHELOT,  294 
BERTHOLLET,  305 
BERZELIUS,  272 
Bodies 

amorphous,  28 

homogeneous,  5 
Boiling,  62 
Boiling  point,  22,  65 

constant,  64 

curve,  190 
BOYLE'S  LAW,  40 
BUNS  EN,  123 


C. 

Calorie,  171 
Capacity  factor 

of  energy,  19 

of  chemical  energy,  264 
Catalyser,  295,  298 

ideal,  299 

negative,  298 

effect  on  equilibrium,  310 
Cation,  332 
Centimetre,  9 
Centrifuge,  56 
Chemical  compounds,  200 
Chemical  energy,  7 

capacity  factor,  264 
Chemical  equilibrium,  302 
Chemical  processes,  5 

general  criteria,  219 

in  the  narrow  sense,  168 

of  the  simplest  kind,  61 

reversibility  of,  171 
Chemistry,  4 
Coefficient  of  expansion,  23 

of  crystals,  31 

of  gases,  42 

of  gas  solutions,  101 

of  liquids,  35 

of  solid  bodies,  30 

of  water,  36 
Cohesion,  305 

Colligative  properties,  265,  275,  287 
Colloidal  solutions,  284 
Combining  weights,  247 

general  meaning  and  importance  of, 
263 

methods  of  determination,  260 

indefmiteness,  262 

of  compound  substances,  253 


343 


344 


INDEX 


Complete  reaction,  259 
Composition,  117 

relation  to  properties,  315 

properties,  continuous  functions  of, 
120 

of  ions,  335 
•  of  phases,  113 
Compounds 

combining  weight  of,  253 
Compressibility,  23 

of  liquids,  34 
Concentration,  277 

molar,  282,  292 
Condenser,  135 
Conservation 

of  the  elements,  173 

of  energy,  6 

of  weight,  12 

of  mass,  14 

Constant  proportions,  Law  of,  226,  247 
Constitution,  324 
Continuity,  Law  of,  175 
Continuous  functions,  24 

of  composition,  245,  293 
Continuous  phenomena,  291 
Convection,  290 
Critical  line,  130 
Critical  point,  73 

for  solutions,  128 
Critical  pressure,  74 
Critical  temperature,  74 
Critical  volume,  74 
Crystalline  liquids,  40 
Crystals,  26 

groups  of,  28 

liquid,  40 

expansibility  of,  31 
Cubic  centimetre,  9 
Cubic  expansion,  31 

D. 

DALTON,  102,  111,  272 
Deduction,  311 
Density,  15 

measurement  of,  37 

of  water,  37 
Diaphragms 

ideal,  104 


Diaphragms 

semi-permeable,  105 
Diffusion,  99,  296 
Dilute  solutions 

properties  of,  273 

reactions  between,  239 
Displacement  of  equilibrium 

Law  of,  83,  151 
Dissociation 

electrolytic,  339 

Dissociation    equilibrium    in    electro- 
lytes, 340 
Distillation,  135 

fractional,  136 

apparatus  for,  137 
Double  decomposition,  168 


E. 

Elasticity,  28 
Elastic  limit,  29 
Electricity,  7 
Electro-chemistry,  7 
Electrodes,  332 
Electrolyte,  332 
Electrolytic  dissociation,  339 
Elementary  analysis,  172 
Elements,  169 
Emulsion,  58 
Energy,  6 

as  criterion  of  chemical  change,  224 

capacity  factor  of,  19 

chemical,  7 

conservation  of,  7 

intensity  factor  of,  19 
Energy  changes  as  criteria  of  chemical 

change  in  solution,  244 
Energy  content,  224 
Entropy,  72 

unit  of,  73 

Equations,  chemical,  258 
Equilibrium,  63 

and  catalyse rs,  310 

between  several  phases,  304 

between  the  three  states,  85 

chemical,  259 

effect  of  pressure  on,  112 

law  of,  85 

liquid-gas,  60 


INDEX 


345 


Equilibrium,  liquid-solid,  80 

quantitative  investigation  of,  308 
solid-solid,  89 
with  solids  t  148 

Equimolar  solutions,  275 

Equivalents,  288 

ESSON,  294 

Eutectic,  156 

Eutectic  point,  155 

Eutectic  solution,  155 

Eutectic  mixture,  155 

Existence  of  possible  substances,  302 

Extrapolation,  178 


Faraday's  Law,  333 

Filtration,  55 

Foams,  59 

Fog,  58 

Formulae,  chemical,  255 

Freedom,  degrees  of,  76 

Freezing,  80 

Freezing  point,  22,  81 
lowering  of  the,  284 
laws  of  lowering  of,  285 


G. 


Gas  constant  applied  to  solutions,  101 
Gas  density,  Law  of,  266 
Gaseous  bodies,  26 
Gaseous  solutions,  97 

of  two  gases,  181 

of  a  gas  and  a  liquid,  186 

of  a  gas  and  a  solid,  186 
Gas  equation,  numerical  values,  271 
Gases,  40 

anomalous,  307 

chemical  combination  between,  202 

density  of,  266 

dissociation  of,  235 

evolution  from  solution,  241 

fractional  separation  of,  105 
Gas  law  for  solutions,  101 
Gas-liquid  equilibrium,  60 
Gas  solutions,  104 


Gas  solutions,  density  of,  101 

properties  of,  103 

of  liquid  substances,  140 

separation   of   the    constituents  of, 
104 

with  liquids,  120 
Gas  volume  law,  265 
GAY-LUSSAC,  42 
Gramme,  11 
GULDBERG,  294 

H. 

HARCOURT,  294 
Heat,  21 

expansion  caused  by,  23 

latent,  70 

unit  of,  71 
Heat  energy 

measurement  of,  71 

quantity  of,  71 
Heat  exchange,  225 
HENRY,  122 
HOFF,  VAN  T',  278 
Homogeneous  bodies,  5 
Hylotropic  transformation,  166. 


I. 


Ideal  catalysers,  299 
Ideal  liquids,  33 
Induction,  311 

incomplete,  123 
Inductive  conclusion,  123 
Inelastic  bodies,  29 
Integral  reactions,  Law  of,  249 
Intensities,  17 

Intensity  factor  of  energy,  19 
Intermediate  products,  298 
Interpolation,  177 
Ions,  331 

chemical  concept  of,  334 

isomerism  of,  332 
Isobar,  131 
Isobaric  change,  60 
Isomerism,  315,  320 

of  ions,  333 

electrolytic,  336 

theory  of,  328 


346 


INDEX 


Isothermal  change,  60 
Isothermal  phase  diagrams,  190 


K. 

Kilogramme,  11 

Kink,    characteristic    of    a    chemical 
compound,  229 


Labile  condition,  80 

Latent  heat,  70 

Limited  solubility  among  liquids,  126 

Limiting  solution,  144 

Linear  expansion,  31 

Liquefaction,  region  of,  133 

point  of,  81 
Liquid  bodies,  26 
Liquid  crystals,  39 
Liquid-gas  equilibrium,  60 
Liquid-liquid  solutions,  123 
Liquid  mixtures,  57 
Liquid-solid  equilibrium,  80 
Liquid 

solution  of  a  gas  and  a,  186 
Liquid  solutions,  53,  97,  118 

from  solid  substances,  152 
Liquids,  32 

chemical  reactions  between,  206 

crystalline,  39 

gaseous  solutions  from,  140 

ideal,  34 

separation  from  solution,  242 

solutions  of  gases  in,  120 

solutions  of  solids  and,  187 


M. 

Magnetism,  7 
Magneto-chemistry,  7 
Manometer,  20 
Mass,  7,  13 

conservation  of,  14 
Mass  action,  Law  of,  305 
Matter,  9,  12 

Maxima     and     minima     in     solution 
curves,  125 


Measurement 

of  density  and  specific  volume,  37 

of  quantity  of  heat,  71 
Mechanics,  7 
Mechanical  properties,  8 
Mechano-chemistry,  7 
Melting,  80 
Melting  point,  81 

effect  of  pressure  on,  82 
curve  of,  83 

solubility  at  the,  158 
Metamerism,  323 
Metastable  condition,  80,  92 
Metastasis,  168 
Metre,  9 
Millimol,  273 
Mixture,  49 
Mixtures 

eutectic,  155 

methods  of  separating,  51 

of  liquids  and  solids,  54 

properties  of,  52 

singular,  147 

with  gases,  58 
Mol,  273 

Molar  concentration,  292 
Molar   concept   in    the   case   of   solid 

solutions,  288 
Molar  weight,  267 

determination  in  the  case  of  soluble 
substances,  286,  287 

of  salts,  337 
Molecular  volumes  and  weights,  289 

N. 

Name,  2 

Natural  Law,  2,  49,  252 
Negative  quantities,  116 

O. 

Observation,  3 

Optics,  7 

Osmotic  pressure,  276 

P. 

Partial  density,  122 
Partial  pressure,  100 


INDEX 


347 


Partially  soluble  liquids 

the  vapour  from,  141 
PEAN  DE  ST.  GILLES,  294 
Phase  Law,  77,  113,  114 

applied  tp  salts,  338 
Phases,  75 

composition  of,  113 
Photo-chemistry,  7 
Physics,  4 
Point,  triple,  85 

eutectic,  155 

critical,  73 
Polymerism,  323 
Polymorphic  forms,  solubility  of,  319, 

320' 

Polymorphism,  317 
Polyvalent  ions,  336 
Porous  diaphragms 

passage  of  gas  solutions  through,  105 
Potential  existence  of  elements,  257 
Prediction,  3 
Pressure,  16 

critical,  74 

effect  on  equilibrium,  112 

effect  on  melting  point,  82 

measurement  of,  20 
Pressure,  osmotic,  276 
Pressures,  scale  of,  20 
Properties 

arbitrary,  3 

as    continuous    functions    of    com- 
position, 103,  119 

colligative,  287 

mechanical,  8 

of  mixtures,  52 

as  related  to  composition,  315 
Proportions,  Law  of  constant,  226,  247 


Q. 

Quantities,  17 

Quantity  factor  of  energy,  19 


R. 

Radical,  325 

Rational  multiples,  Law  of,  254 

Reactions,  Law  of  integral,  249 


Reaction  velocity,  290,  291 
effect  of  solvent  on,  297 
effect  of  temperature  on,  297 
Law  of,  294 

Regular  crystals,  32 

Relative  weight,  9 

Retort,  135 

Reversible  chemical  reactions,  171 

Reversibility,  62 


S. 
Salts,  331 

phase  rule  applied  to,  338 

molar  weight  of,  337 
Saturated  vapour,  65 
Saturation,  64 

phenomena  of,  149 

Saturation  equilibrium,  effect  of  tem- 
perature on,  113 
Saturation  distribution,  150 
Secondary  reactions,  298 
Semi-permeable  diaphragms,  105 
Sense  impressions,  1 
Separation,   of    liquid    solutions   into 
components,  130 

of  gaseous  solutions,  104 
Singular  mixture,  147,  165 

point,  163 

solution,  138 

value,  126 
Solid  bodies,  26 

chemical  reaction  between,  208 
Solidification,  80 
Solid-liquid     equilibrium,     effect    of 

pressure  on,  82 
Solid  phase,  and  a  solution,  148 
Solid,  separation  from  solution,  243 
Solid-solid  equilibrium,  89 
Solid  solutions,  54,  97 

molar  concept  in  the  case  of,  289 
Solid  substance 

effect  of  pressure  and  temperature 
on  the  solubility  of  a,  150 

liquid  solutions  from  a,  152 

solution  of  a  gas  and  a,  187 

solution  of  a  liquid  and  a,  186 
Solid  substances 

solutions  of  two,  153 


348 


INDEX 


Solubility 

at  the  melting  point,  158 

curve,  124 

effect  of  pressure  and  temperature 
on,  150 

limited,  126 

of  allotropic  forms,  161 

of  polymorphic  forms,  320 
Solute,  120 
Solution  Law,  286 
Solutions,  61,  63,  96 

and    pure    substances    as    limiting 
cases,  109 

equimolar,  275 

from  phases  in  the  same  state,  181 

from  phases  of  unlike  states,  186 

gas-liquid,  120 

liquid,  53,  118 

liquid,  from  solid  substances,  152 

liquid-liquid,  123 

liquid,  separation,  130 

of  higher  order,  162 

of  one  gas  and  one  liquid,  186 

of  one  gas  and  one  solid,  186 

of  one  solid  and  one  liquid,  187 

of  two  gases,  181 

of  two  liquids,  182 

of  two  solid  substances,  183 

properties  of  dilute,  273 

reactions  between  dilute,  239 

singular,  138 

solid,  54,  97 

vapour  of,  131 

with  a  solid  phase,  148 
Solvent,  120 

effect  on  reaction  velocity,  297 
Specific  gravity,  15 
Specific  properties,  3 
Specific  volume,  15 
Stability  of  polymorphic  forms,  319 

region  of,  167 
State  of  aggregation,  315 

changes  of,  60 
States,  26,  47 
Structure  theory,  325,  329 
Sublimation,  78 
Substance,  47 

Law,  48 
Substances,  4 


Substances,  pure,  61,  63 

pure,  definition  of,  109 

undecomposed,  169 
Supercooling,  83 
Supersaturation,  65,  80 
Surface,  clean,  57 
Surface  energy,  29,  32 

molar,  288 
Surface  layer,  56 
Surface  representing  one  phase,  189 

representing  two  phases,  189 
Surface  tension,  32 
Suspended  transformation,  79,  318 

phenomena  of,  90 
Synthesis,  172 

Synthetic  processes,  168,  174 
Systems  of  the  first  order,  117 


T. 

Temperature,  21 

absolute,  43 

critical,  74 

effect  on  reaction  velocity,  297 

effect  on  saturation  equilibrium,  113 

eutectic,  155 

Temperature  pressure,  25 
Ternary  systems,  239 
Thermics,  7 

Thermo-chemistry,  7,  71 
Thermometer,  21 

Transition,  from  one  state  to  another, 
60 

hylotropic,  166 

temperature,  90 
Transition  point,  vapour  pressure  at, 

94 

Triaxial  crystals,  32 
Triple  point,  85 


U. 

Undecomposed  substances   169 

Uniaxial  crystals,  32 

Unit  of  volume,  9 

Units  of  combining  weights,  272 

Univalent  ions,  336 

Unlimited  solubility,  123 


INDEX 


349 


Unsaturated  vapour,  64 
Unstable  forms,  90 


V. 

Valence,  326 
Vaporization,  62 

change  of  volume  during,  68 

heat  of,  70 

heat  of,  of  water,  72 

region  of,  133 
Vapour,  62 

of  partially  soluble  liquids,  141 

of  solutions,  131 

saturated,  64 

unsaturated,  64 
Vapour  pressure,  6,5 

and  osmotic  pressure,  281 

molar  lowering  of,  275 

of  water,  65 
Vapour  pressure  curves,  67 

at  the  triple  point,  88 
Vapour  pressure  of  allotropic  forms,  9: 
Velocity,  chemical,  291 

variable,  293 
Viscosity,  29,  33 
Volume,  7 

critical,  74 


Volume,  measurement  of,  37 

specific,  15 

unit  of,  9 

Volume  change  among  solid  bodies,  30 
Volume  energy,  16 
Volume  expansion,  31 
Volumetric  analysis,  264 


W. 

WAAGE,  294 
Water, 

density  and  specific  volume  of,  37 

expansibility  of,  36 

heat  of  vaporization  of,  72 

vapour  pressure  of,  65 
Weight,  7,  10 

absolute,  10 

conservation  of,  12 

relative,  10 

unit  of,  10 
WENZEL,  294 
WILHELMY,  294 
Word,  2 
Work,  6 

Z. 

Zero,  absolute,  43 


OCT 


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